Acts 16

As Paul was directed to teach in a vision to teach the gospel in Macedonia, we witness two conversions and the conditions of those conversions.  First -

"...a certain woman named Lydia, a seller of purple, of the city of Thyatira, which worshipped God, heard us: whose heart the Lord opened, that she attended unto the things which were spoken of Paul.
15 And...she was baptized, and her household..."  New Testament | Acts 16:14 - 15)

Second was a Paul and Silas were cast into jail where -

"...at midnight Paul and Silas prayed, and sang praises unto God: and the prisoners heard them.
26 And suddenly there was a great earthquake, so that the foundations of the prison were shaken: and immediately all the doors were opened, and every one's bands were loosed.
27 And the keeper of the prison awaking out of his sleep, and seeing the prison doors open, he drew out his sword, and would have killed himself, supposing that the prisoners had been fled.
28 But Paul cried with a loud voice, saying, Do thyself no harm: for we are all here.
29 Then he called for a light, and sprang in, and came trembling, and fell down before Paul and Silas,
30 And brought them out, and said, Sirs, what must I do to be saved?
31 And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
32 And they spake unto him the word of the Lord, and to all that were in his house.
33 And he took them the same hour of the night, and washed their stripes; and was baptized, he and all his, straightway.
34 And when he had brought them into his house, he set meat before them, and rejoiced, believing in God with all his house."  (New Testament | Acts 16:25 - 34)

I note that the Jailer asked "what must I do to be saved?"  Herein we witness the conditions of the  first principles and ordinances of the gospel where both the Jailer and Lydia with there households believed and were baptized.

The Prophet Joseph Smith explained -

"We believe that the first principles and ordinances of the Gospel are: first, Faith in the Lord Jesus Christ; second, Repentance; third, Baptism by immersion for the remission of sins; fourth, Laying on of hands for the gift of the Holy Ghost."  (Pearl of Great Price | Articles of Faith 1:4)