2 Nephi 29 - 32

As Nephi comes to his last writings in his small plates, he says there are -

"...a few words which I must speak concerning the doctrine of Christ; wherefore, I shall speak unto you plainly..." (Book of Mormon 2 Nephi 31:2)

He speaks of repentance and baptism then follows -

"...I know that if ye shall follow the Son, with full purpose of heart, acting no hypocrisy and no deception before God, but with real intent, repenting of your sins, witnessing unto the Father that ye are willing to take upon you the name of Christ, by baptism—yea, by following your Lord and your Savior down into the water, according to his word, behold, then shall ye receive the Holy Ghost; yea, then cometh the baptism of fire and of the Holy Ghost; and then can ye speak with the tongue of angels, and shout praises unto the Holy One of Israel." (Book of Mormon 2 Nephi 31:13)

What is this - the "tongue of angels"? First Nephi reminds us -

"...Do ye not remember that I said unto you that after ye had received the Holy Ghost ye could speak with the tongue of angels? And now, how could ye speak with the tongue of angels save it were by the Holy Ghost?" (Book of Mormon 2 Nephi 32:2)

"Angels speak by the power of the Holy Ghost; wherefore, they speak the words of Christ..." (Book of Mormon 2 Nephi 32:3)

So to speak with the tongue of angels we must be worthy and receive the Holy Ghost. We must also come to understand and speak the words of Christ. To do that, Nephi admonishes us -
"...feast upon the words of Christ..." (Book of Mormon 2 Nephi 32:3)

For it is -

"...the words of Christ will tell you all things what ye should do." (Book of Mormon 2 Nephi 32:3)
And if we cannot understand the words of Christ -

"...it will be because ye ask not, neither do ye knock..." (Book of Mormon 2 Nephi 32:4)

And as we study and come to understand the words of Christ through prayer and by feasting upon the scriptures, then when we speak the words of Christ with the Spirit, we speak with the tongues of angels.

"Wherefore, he that preacheth and he that receiveth, understand one another, and both are edified and rejoice together." (Doctrine and Covenants Section 50:22)