Authority

Experience

Prophets

Nothing trumps the authority of a first hand experience with God, that is how prophets were called:

5 Wherefore it came to pass that my father, Lehi, as he went forth prayed unto the Lord, yea, even with all his heart, in behalf of his people.
6 And it came to pass as he prayed unto the Lord, there came a pillar of fire and dwelt upon a rock before him; and he saw and heard much; and because of the things which he saw and heard he did quake and tremble exceedingly.
7 And it came to pass that he returned to his own house at Jerusalem; and he cast himself upon his bed, being overcome with the Spirit and the things which he had seen.
8 And being thus overcome with the Spirit, he was carried away in a vision, even that he saw the heavens open, and he thought he saw God sitting upon his throne, surrounded with numberless concourses of angels in the attitude of singing and praising their God.
9 And it came to pass that he saw One descending out of the midst of heaven, and he beheld that his luster was above that of the sun at noon-day.
10 And he also saw twelve others following him, and their brightness did exceed that of the stars in the firmament.
11 And they came down and went forth upon the face of the earth; and the first came and stood before my father, and gave unto him a book, and bade him that he should read.
12 And it came to pass that as he read, he was filled with the Spirit of the Lord.
13 And he read, saying: Wo, wo, unto Jerusalem, for I have seen thine abominations! Yea, and many things did my father read concerning Jerusalem – that it should be destroyed, and the inhabitants thereof; many should perish by the sword, and many should be carried away captive into Babylon.
14 And it came to pass that when my father had read and seen many great and marvelous things, he did exclaim many things unto the Lord; such as: Great and marvelous are thy works, O Lord God Almighty! Thy throne is high in the heavens, and thy power, and goodness, and mercy are over all the inhabitants of the earth; and, because thou art merciful, thou wilt not suffer those who come unto thee that they shall perish!
15 And after this manner was the language of my father in the praising of his God; for his soul did rejoice, and his whole heart was filled, because of the things which he had seen, yea, which the Lord had shown unto him.
16 And now I, Nephi, do not make a full account of the things which my father hath written, for he hath written many things which he saw in visions and in dreams; and he also hath written many things which he prophesied and spake unto his children, of which I shall not make a full account.
17 But I shall make an account of my proceedings in my days. Behold, I make an abridgment of the record of my father, upon plates which I have made with mine own hands; wherefore, after I have abridged the record of my father then will I make an account of mine own life.
18 Therefore, I would that ye should know, that after the Lord had shown so many marvelous things unto my father, Lehi, yea, concerning the destruction of Jerusalem, behold he went forth among the people, and began to prophesy and to declare unto them concerning the things which he had both seen and heard. (1 Nephi 1) 

Apostles

The call of the apostle Paul was a direct result of his encounter with Jesus Christ:

3 And as he journeyed, he came near Damascus: and suddenly there shined round about him a light from heaven:
4 And he fell to the earth, and heard a voice saying unto him, Saul, Saul, why persecutest thou me?
5 And he said, Who art thou, Lord? And the Lord said, I am Jesus whom thou persecutest: it is hard for thee to kick against the pricks.
6 And he trembling and astonished said, Lord, what wilt thou have me to do? And the Lord said unto him, Arise, and go into the city, and it shall be told thee what thou must do.
7 And the men which journeyed with him stood speechless, hearing a voice, but seeing no man.
8 And Saul arose from the earth; and when his eyes were opened, he saw no man: but they led him by the hand, and brought him into Damascus.
9 And he was three days without sight, and neither did eat nor drink.
10 And there was a certain disciple at Damascus, named Ananias; and to him said the Lord in a vision, Ananias. And he said, Behold, I am here, Lord.
11 And the Lord said unto him, Arise, and go into the street which is called Straight, and enquire in the house of Judas for one called Saul, of Tarsus: for, behold, he prayeth,
12 And hath seen in a vision a man named Ananias coming in, and putting his hand on him, that he might receive his sight.
13 Then Ananias answered, Lord, I have heard by many of this man, how much evil he hath done to thy saints at Jerusalem:
14 And here he hath authority from the chief priests to bind all that call on thy name.
15 But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:
16 For I will shew him how great things he must suffer for my name’s sake.
17 And Ananias went his way, and entered into the house; and putting his hands on him said, Brother Saul, the Lord, even Jesus, that appeared unto thee in the way as thou camest, hath sent me, that thou mightest receive thy sight, and be filled with the Holy Ghost.
18 And immediately there fell from his eyes as it had been scales: and he received sight forthwith, and arose, and was baptized. (Acts 9)

1 Paul, an apostle, (not of men, neither by man, but by Jesus Christ, and God the Father, who raised him from the dead;) 
11 But I certify you, brethren, that the gospel which was preached of me is not after man.
12 For I neither received it of man, neither was I taught it, but by the revelation of Jesus Christ.
13 For ye have heard of my conversation in time past in the Jews’ religion, how that beyond measure I persecuted the church of God, and wasted it:
14 And profited in the Jews’ religion above many my equals in mine own nation, being more exceedingly zealous of the traditions of my fathers.
15 But when it pleased God, who separated me from my mother’s womb, and called me by his grace,
16 To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood:
17 Neither went I up to Jerusalem to them which were apostles before me; but I went into Arabia, and returned again unto Damascus.
18 Then after three years I went up to Jerusalem to see Peter, and abode with him fifteen days.
19 But other of the apostles saw I none, save James the Lord’s brother. (Galatians 1)

Elders 

Elders were called “Elders” because their age and/or their experience with God:  

22 And he spake unto me concerning the elders of the Jews (1 Nephi 4; v. 27)

37 who are his elder brethren. (1 Nephi 16)

7 The elder was called Jacob and the younger Joseph. (1 Nephi 18)

7 Alma had consecrated to be teachers, and priests, and elders over the church (Alma 4)

16 And he selected a wise man who was among the elders of the church (Alma 4)

Holy Spirit

It is a fact that wheresoever the Holy Spirit is, God is, and such stand approved of God, for His Spirit confirms truth and holiness and is called “The Holy Spirit of Promise.” (Eph. 1:13)

Name of Jesus

The authority to command elements, cast out devils, perform miracles, pray to God, baptize, ordain and name a church is contained in the name of Jesus, and ANY follower of Christ is allowed to use his name.

New Testament

23 And in that day ye shall ask me nothing. Verily, verily, I say unto you, Whatsoever ye shall ask the Father in my name, he will give it you.
24 Hitherto have ye asked nothing in my name: ask, and ye shall receive, that your joy may be full. (John 16)

18 And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth.
19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
20 Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen. (Matthew 18)

Command the Elements

6 Wherefore, we search the prophets, and we have many revelations and the spirit of prophecy; and having all these witnesses we obtain a hope, and our faith becometh unshaken, insomuch that we truly can command in the name of Jesus and the very trees obey us, or the mountains, or the waves of the sea. (Jacob 4)

Cast Out Devils

19 And in the name of Jesus did he cast out devils and unclean spirits; and even his brother did he raise from the dead, after he had been stoned and suffered death by the people.
20 And the people saw it, and did witness of it, and were angry with him because of his power; and he did also do many more miracles, in the sight of the people, in the name of Jesus. (3 Nephi 7)

Miracles

1 And now it came to pass that according to our record, and we know our record to be true, for behold, it was a just man who did keep the record – for he truly did many miracles in the name of Jesus; and there was not any man who could do a miracle in the name of Jesus save he were cleansed every whit from his iniquity – (3 Nephi 8)

5 And there were great and marvelous works wrought by the disciples of Jesus, insomuch that they did heal the sick, and raise the dead, and cause the lame to walk, and the blind to receive their sight, and the deaf to hear; and all manner of miracles did they work among the children of men; and in nothing did they work miracles save it were in the name of Jesus. (4 Nephi 1)

Ask God

27 O then despise not, and wonder not, but hearken unto the words of the Lord, and ask the Father in the name of Jesus for what things soever ye shall stand in need. Doubt not, but be believing, and begin as in times of old, and come unto the Lord with all your heart, and work out your own salvation with fear and trembling before him. (Mormon 9)

Pray

6 And the twelve did teach the multitude; and behold, they did cause that the multitude should kneel down upon the face of the earth, and should pray unto the Father in the name of Jesus.
7 And the disciples did pray unto the Father also in the name of Jesus. And it came to pass that they arose and ministered unto the people. (3 Nephi 19)

Ordain

3 In the name of Jesus Christ I ordain you to be a priest, (or, if he be a teacher) I ordain you to be a teacher, to preach repentance and remission of sins through Jesus Christ, by the endurance of faith on his name to the end. Amen. (Moroni 3)

Baptize

11 And the Father said: Repent ye, repent ye, and be baptized in the name of my Beloved Son.
12 And also, the voice of the Son came unto me, saying: He that is baptized in my name, to him will the Father give the Holy Ghost, like unto me; wherefore, follow me, and do the things which ye have seen me do. (2 Nephi 31)

23 Verily I say unto you, that whoso repenteth of his sins through your words, and desireth to be baptized in my name, on this wise shall ye baptize them – Behold, ye shall go down and stand in the water, and in my name shall ye baptize them.
24 And now behold, these are the words which ye shall say, calling them by name, saying:
25 Having authority given me of Jesus Christ, I baptize you in the name of the Father, and of the Son, and of the Holy Ghost. Amen.
26 And then shall ye immerse them in the water, and come forth again out of the water.
27 And after this manner shall ye baptize in my name; for behold, verily I say unto you, that the Father, and the Son, and the Holy Ghost are one; and I am in the Father, and the Father in me, and the Father and I are one. (3 Nephi 11)

Church Called

7 Therefore, whatsoever ye shall do, ye shall do it in my name; therefore ye shall call the church in my name; and ye shall call upon the Father in my name that he will bless the church for my sake.
8 And how be it my church save it be called in my name? For if a church be called in Moses’ name then it be Moses’ church; or if it be called in the name of a man then it be the church of a man; but if it be called in my name then it is my church, if it so be that they are built upon my gospel.
9 Verily I say unto you, that ye are built upon my gospel; therefore ye shall call whatsoever things ye do call, in my name; therefore if ye call upon the Father, for the church, if it be in my name the Father will hear you; (3 Nephi 27)

Preordination

5 Before I formed thee in the belly I knew thee; and before thou camest forth out of the womb I sanctified thee, and I ordained thee a prophet unto the nations. (Jeremiah 1)

Priesthood

The authority to act for God shifted from priestly blood lines to all faithful believers in Christ. Anyone could use his name. Jesus demonstrated that when he declined to stop a non-disciple from using his name to perform miracles:

38 And John answered him, saying, Master, we saw one casting out devils in thy name, and he followeth not us : and we forbad him, because he followeth not us.
39 But Jesus said, Forbid him not : for there is no man which shall do a miracle in my name, that can lightly speak evil of me.
40 For he that is not against us is aon our part. (Mark 9)

Witnesses

18 Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven.
19 Again I say unto you, That if two of you shall agree on earth as touching any thing that they shall ask, it shall be done for them of my Father which is in heaven.
20 For where two or three are gathered together in my name, there am I in the midst of them. (Matthew 18)