Baptism as taught in the bible.
There are several baptisms mentioned in the bible, such as the baptism of fire, the baptism of the Holy Spirit, the baptism of suffering, and the baptism of John. However, the particular baptism ordained in the great commission and the one submitted to by those becoming a part of the new covenant is the baptism which is now in force and which will ever be throughout this dispensation .
Just prior to His ascension Jesus commissioned his disciples to baptize
” And Jesus came and spoke to them saying, “All authority has been given to Me in heaven and on earth. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things that I have commanded you; and lo I am with you always, even to the end of the age.” (Matthew 28:18-20).

This baptism was water baptism.
There are those who teach that the baptism of the great commission is Holy Spirit baptism, but this cannot be, for the passage shows that the disciple were to do both the teaching and baptizing, whereas only Jesus is said in the scripture to be the administrator of Holy Spirit baptism. From a study in Acts, it is seen that the baptism with which they baptized men was water baptism. Philip baptized the Eunuch in water (Acts 8:36-39). Cornelius and his household were baptized in water (Acts 10:47).

Faith and repentance must precede bible baptism.
Whom did Jesus command His disciples to baptize? Those whom they had taught (Matt 28:19). What comes before baptism in Mark 16:15, 16? The hearing of the gospel of faith. What commandment did Peter make before baptism in Acts 2:38? Repentance! What condition of heart were those people in whom Peter commanded to repent and be baptized? They had heard him preach Christ and were cut to the heart (Acts 2:22-37). When did the Samaritans submit to baptism? After they believed the things Philip preached (Acts 8:12). What preceded the Eunuchs baptism? He had heard Philip preach Jesus and desired baptism (Acts 8:26-39). Case upon case throughout the book of Acts could be cited showing that those baptized were prepared for it by hearing about Christ, believing on Him, and repenting of their sins. Therefore, we understand that Christ did not intend for infants who cannot learn of Christ, who cannot believe on Him, and who cannot repent to be baptized. There is not a case on divine record where an infant was baptized. And we also understand that adults who refuse to learn of Christ, who refuse to truly believe on Him, or who refuse to repent of their sins are not fit subjects to be scripturally baptized. Though they may be immersed, yet without these necessary prerequisites, the promise connected with scriptural baptism do not belong to them, for they have not been scripturally baptized.

Baptism is the dividing line between the old life and the new. Between the state of condemnation and the state of salvation.
Jesus said, “He who believes and is baptized shall be saved” (Mark 16:16). On Pentecost, Peter promised those who would repent and be baptized would receive the remission of sins and the gift of the Holy Spirit, and we notice that those who obediently received Peter’s words were added to the church by the Lord (Acts 2:38-41,47). Ananias told Saul of Tarsus to be baptized for the remission of sins (Acts 22:6). Peter pointed out the fact that baptism has to do with our salvation (IPet 3:20,21). Paul said that we are baptized into Christ (Gal 3:27). He also said that we are baptized into the body, the church (ICor 12:13). Jesus said that except one be born of the water and the Spirit, he cannot enter the kingdom of God (John 3:5). And the entire 6th chapter of Romans shows that baptism is the dividing line between the old life of sin and the new life of righteousness. This bible teaching completely sets aside the teaching that baptism has nothing to do with salvation. Jesus ordained it to have a vital connection with salvation, so the apostles preached it, and thus we believe it.

This baptism is an immersion – a burial.
Romans 6:3,4 and Colossians 2:12 both state this. Every case of water baptism is recorded, whether the baptism of John or the baptism of the great commission, coincides with the practice of immersion. John baptized in Aenon near Salem because there was much water there (John 3:23). The preacher and the candidate both went down into the water for the immersion, and following they came up out of the water (Acts8:38; Mark 1:9,10). The bible alludes to figures of speech and expressions that are only harmonious with immersion. For instance, the figure of birth is used in John 3:5, and a birth is a coming out of something larger than one born. It is referred to as a burial in Colossians 2:12. It is referred to as the washing of the body in Hebrews 10:22. And last, but not least, the meaning of the Greek word which Jesus used to refer to this act and which is translated “baptism” means to plunge, dip, immerse”. Every Greek dictionary will so state. even large, unabridged English dictionaries that give the root meaning of our words give the meaning of burial and immersion. The practice of sprinkling or pouring did not begin from the teaching of the bible.

The new life following baptism.
One in Christ is a “New Creature”, and he/she is to walk in newness of life (II Cor 5:17; Rom 6:4). Those risen with Christ are to seek things above, setting their affection on those things instead of the things of earth (Col 3:1).

Scripture reference:
Matthew 28:18-20 And Jesus came and spoke to them saying, “All authority has been given to Me in heaven and on earth. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things that I have commanded you; and lo I am with you always, even to the end of the age.”
Mark 16:16 “He who believes and is baptized will be saved; but who does not believe will be condemned.”
John 3:5 Jesus answered, “Most assuredly, I say unto you, unless one is born of water and the spirit, he cannot enter the kingdom of God.”
Acts 2:38 “Then Peter said to the, “Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins, and you shall receive the gift of the Holy Spirit.”
Acts 8:36-39 “Now as they went down the road, they came to some water. And the Eunuch said, “See, here is water. What hinders me from being baptized?” Then Philip said, “If you believe with all your heart, you may.” And he answered and said, “I believe that Jesus Christ is the Son of God.” So he commanded the chariot to stand still. And both Philip and the Eunuch went down into the water, and he baptized him.”
Acts 16:33 “And he took them the same hour of the night and washed their stripes. And immediately he and all his family were baptized.”
Romans 6:4-6 “Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life. For if we have been united together in the likeness of His death, certainly we also shall be in the likeness of His resurrection, knowing this, that our old man was crucified with Him, that the body of sin might be done away with, that we should no longer be slaves of sin.”
Colossians 2:12 “buried with Him in baptism, in which you also were raised with Him through faith in the working of God, who raised Him from the dead.”
1 Peter 3:21 “There is also an antitype which now saves us – baptism (not the removal of filth of the flesh, but the answer of a good conscience towards God), through the resurrection of Jesus Christ,”
Lesson taken from “Simple Stimulating Studies” by Donald Hunt.

Baptisms at White Plains Church Link.