Helaman 15

We learn a pattern of true conversion as Samuel the Lamanite speaks of his own people as -

"...salvation hath come unto them through the preaching of the Nephites; and for this intent hath the Lord prolonged their days.
5 And I would that ye should behold that the more part of them are in the path of their duty, and they do walk circumspectly before God, and they do observe to keep his commandments and his statutes and his judgments according to the law of Moses." (Book of Mormon | Helaman 15:4 - 5)

And -

"...the more part of them are doing this, and they are striving with unwearied diligence that they may bring the remainder of their brethren to the knowledge of the truth; therefore there are many who do add to their numbers daily." (Book of Mormon | Helaman 15:6)

"...for ye have witnessed it, that as many of them as are brought to the knowledge of the truth, and to know of the wicked and abominable traditions of their fathers, and are led to believe the holy scriptures, yea, the prophecies of the holy prophets, which are written, which leadeth them to faith on the Lord, and unto repentance, which faith and repentance bringeth a change of heart unto them—
8 Therefore, as many as have come to this, ye know of yourselves are firm and steadfast in the faith, and in the thing wherewith they have been made free." (Book of Mormon | Helaman 15:7 - 8)

That is conversion means repentance, having a change of heart, keeping the commandments, sharing the gospel, studying and followinging the scriptures and words of the living prophets, and remaining firm, steadfast, and immovable. They even remove from their lives and "natural man" temptations that may allow them to return to inquity as the Lamanites -

"...buried their weapons of war, and they fear to take them up lest by any means they should sin..." (Book of Mormon | Helaman 15:9)

In summary -

"And now, because of their steadfastness when they do believe in that thing which they do believe, for because of their firmness when they are once enlightened, behold, the Lord shall bless them and prolong their days..." (Book of Mormon | Helaman 15:10)