Baptisms can be broken down into two (2) main categories:
In the Experiential category, there are two main Baptisms that everyone should experience: Water Baptism and the Baptism of the Holy Spirit. The Lord Jesus has set the example by being Water Baptized by John the Baptist.
13 Then cometh Jesus from Galilee to Jordan unto John, to be baptized of him. 14 But John forbad him, saying, I have need to be baptized of thee, and comest thou to me? 15 And Jesus answering said unto him, Suffer it to be so now: for thus it becometh us to fulfil all righteousness. Then he suffered him.
Water Baptism is a public demonstration of your obedience to the LORD, it shows symbolically the death and burial of the old man and the resurrection into the newness of life. For the proper execution of this activity, the entire body of the person must be submerged in water. Water Baptism is only relevant for persons who have made a conscious decision to accept Jesus Christ as their personal Lord and Saviour. Therefore babies and very small children should not be baptized.
The second Baptism that every single believer in Christ should experience is the Baptism of the Holy Spirit. This Baptism is evidenced by the speaking in tongues.
5 For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence.
It is instructive to note that the account of the initial entry of the Holy Spirit as recorded in Acts 2 was the fulfillment of a commitment that the Lord Jesus made to all of his disciples, so that His chosen and beloved people would not be left comfortless.
15 If ye love me, keep my commandments. 16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever; 17 Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you. 18 I will not leave you comfortless: I will come to you.
Now this promise is still in effect. In these last days, it is critical that every single believer experience the Baptism of the Holy Spirit, with the evidence of speaking with new tongues. If you do not have this in-filling, your oil level (anointing) may not be sufficiently high enough for you to qualify as a suitable candidate for the Rapture.
Even in the Book of Acts, the initial notion was that only Jews were to receive the baptism of the Holy Spirit. Hence the Apostle Peter and others of the circumcision were astonished when the centurion Cornelius and those of his household began to speak with new tongues.
44 While Peter yet spake these words, the Holy Ghost fell on all them which heard the word. 45 And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. 46 For they heard them speak with tongues, and magnify God. Then answered Peter, 47 Can any man forbid water, that these should not be baptized which have received the Holy Ghost as well as we? 48 And he commanded them to be baptized in the name of the LORD. Then prayed they him to tarry certain days.
Do not believe the lie that the Baptism of the Holy Spirit is not for today. It is a must for each and every single believer.
There are two(2) more Experiential Baptisms, but these are special purpose Baptisms, they are the Baptism of Fire [Matthew 3:11] and the Baptism of Suffering [Luke 12:50]. Next, there is the Organizational Baptism, there is only one baptism in this category.
4 There is one body, and one Spirit, even as ye are called in one hope of your calling; 5 One Lord, one faith, one baptism, 6 One God and Father of all, who is above all, and through all, and in you all.
The one baptism here refers to the Organizational Baptism, wherewith you become a member of the body of Christ. The uniqueness about this baptism is that your nature is changed in a similar fashion like when you dye a garment or pickle a vegetable. There is a processing that takes place, and the changes are irreversible. The Holy Spirit is the one who is responsible for the administration of the body and the assignment of the members of that body. There is also the assignment of the Gifts of the Spirit for the various members to function accordingly.
I Corinthians 12:13-14
13 For by one Spirit are we baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit. 14 For the body is not one member but many.