There is no explicit teaching regarding baptism in the scriptures the way we might like to see it. We must accept the fact that God does all things perfectly, so if God wanted us to have such a teaching, I believe that either He would have given such teaching or led one of the early apostles to do so. However, we do have many accounts that mention both water and Spirit baptism, and we can look at these accounts, asking God to guide us in putting them together and drawing a proper conclusion in truth. I will not comment on every account of baptism in Acts, but try to draw truth from the ones that are recounted in more detail.
The baptism at Samaria: (Acts 8:9-25) The second account we have in Acts that mentions baptism is the account of Philip with Simon and the believers at Samaria. We are told that Philip baptized Simon the sorcerer and some other believers. We are specifically told that the believers did not receive the Holy Spirit when they were water baptized, and from the actions of Simon later, I think we may conclude that he did not either. Peter and John were then sent to Samaria, that the believers there might receive the Spirit. From this account I think we can safely conclude that the Holy Spirit is not automatically given because a person is water baptized. From other accounts I believe we will see that the baptisms can (and should) go together, but that there is no "automatic" connection. They are distinct acts of faith before God.
The Ethiopian eunuch: (Acts 8:26-38) Philip was an evangelist, and under the divine direction of the Spirit preached the gospel to this man. The eunuch received the word and asked Philip if he could be baptized. Philip said, "If you believe with all your heart, you may," and based on the response of the eunuch, he baptized him in water. There was no detailed instruction in special classes, or a long period of waiting, but only a "heart of belief." The conclusion that I draw from this account is that the prerequisite of water baptism is simply a wholehearted response to Jesus as Savior. Water baptism here was a declaration of belief in Jesus.
Conversion of Saul: (Acts 9:10-19, 22:12-16) In the accounts of the conversion of Saul, we see that three things happened: 1) Paul received his sight; 2) he was water-baptized; and 3) he received the Holy Spirit. The exact order is not explicitly stated, but it appears that they all happened during the one visit of Ananias. There was no long waiting for any of them. In my understanding, it is God's intention that water baptism and Spirit baptism should go together. We will see this in other accounts to follow. Later, we will try to see some reasons why they may not be together (as at Samaria), but if there are no hindrances, I believe the scriptures teach that they can be expected to occur together.
Conversion of Cornelius: (Acts 10:1-11:18) This was a critical event in the birth of the church because these were the first Gentiles that were baptized with the Spirit into Christ. The account is recorded with considerable detail, but let's just note several points relevant to our topic. I think the most important one is that the believers were baptized with the Holy Spirit simply from the proclamation of the gospel. They were also water baptized, but after they were baptized with the Spirit. From this I believe we can conclude that water baptism is not a requirement for Spirit baptism. Secondly, even though they had already been baptized with the Spirit, Peter proceeded to baptize them with water. Unless we feel that Peter was wrong, I think this shows that we should not dismiss water baptism even if we have been baptized with the Spirit. (We will look at the reasons for water baptism later.) Thirdly, I would draw attention to the fact that the Spirit baptism is described in various ways as: "the Holy Spirit fell on them," "the gift of the Holy Spirit was poured out," "received the Holy Spirit as we have," "baptized with the Holy Spirit," and "gave them the same gift." All of these terms or phrases refer to the same experience.
The disciples at Ephesus: (Acts 19:1-7) We will pass over the accounts of Lydia, the jailer, and the Corinthians, and look in more detail at this account of Paul at Ephesus. I believe this account is particularly important because three baptisms are mentioned (John's baptism, baptism in the name of Jesus, and Spirit baptism). When Paul found these disciples, he asked them a question: "Did you receive the Holy Spirit when you believed?" Why did he ask the question? I would say it was because he detected a lack in their relationship with God and was probing to find out what was missing. They answered that they did not know about the Spirit, so he went farther back and asked, "Into what were you then baptized?" The implication of this question is that if they had been baptized in the name of the Lord Jesus, the baptism with the Holy Spirit should have been known and accompanied that baptism. Although the account does not explicitly say so, I think we can safely conclude that Paul explained the gospel to them, and as a result of their response, he baptized them in water "in the name of the Lord Jesus." He then prayed for them and they received the Holy Spirit. (As a side note, if water baptism was to be done away with, this was certainly a good place for Paul to do that.)
There are several conclusions I think we can draw from this account. First, I think we can say that Paul was most concerned about the Spirit baptism. That was the lack he detected in the beginning. Secondly, Paul obviously expected that if they had been baptized in the name of Jesus, they should also have received the Spirit. Thirdly, we note that just because they were baptized in the name of Jesus they did not automatically receive the Holy Spirit. Paul specifically prayed for them to receive the Holy Spirit. When they did, there was additional evidence that the prayer was answered.
In summary, from the various accounts in Acts I think we can draw the following conclusions:
Water baptism was continued from Pentecost onward. We do not see any indication that it was discontinued by any of the apostles.
Water baptism after Pentecost was different from John's baptism. It was not just a statement of repentance, but also a statement of belief in the Lord Jesus for the forgiveness of sin.
Spirit baptism normally accompanied water baptism. However, it was not automatic and there was no specific order. Sometimes Spirit baptism came before and sometimes after water baptism. Where Spirit baptism did not occur with water baptism, action was taken to correct the condition.