John's Water Baptism
There is John's, a water baptism of repentance for the forgiveness of sins:
1 In the fifteenth year of the reign of Tiberius Caesar, Pontius Pilate being governor of Judea, and Herod being tetrarch of Galilee, and his brother Philip tetrarch of the region of Ituraea and Trachonitis, and Lysanias tetrarch of Abilene, 2 during the high priesthood of Annas and Caiaphas, the word of God came to John the son of Zechariah in the wilderness. 3 And he went into all the region around the Jordan, proclaiming a baptism of repentance for the forgiveness of sins.
(Luke 3, also Matthew 3:1-5; Mark 1:1-8; John 1:19-28; Acts 18:25) [ESV]
Baptism of the Holy Spirit
There is a baptism with the Holy Spirit:
4 And while staying with them he ordered them not to depart from Jerusalem, but to wait for the promise of the Father, which, he said, “you heard from me; 5 for John baptized with water, but you will be baptized with the Holy Spirit not many days from now.” (Acts 1)
1 When the day of Pentecost arrived, they were all together in one place. 2 And suddenly there came from heaven a sound like a mighty rushing wind, and it filled the entire house where they were sitting. 3 And divided tongues as of fire appeared to them and rested on each one of them. 4 And they were all filled with the Holy Spirit and began to speak in other tongues as the Spirit gave them utterance. (Acts 2)
44 While Peter was still saying these things, the Holy Spirit fell on all who heard the word. 45 And the believers from among the circumcised who had come with Peter were amazed, because the gift of the Holy Spirit was poured out even on the Gentiles. 46 For they were hearing them speaking in tongues and extolling God. Then Peter declared, 47 “Can anyone withhold water for baptizing these people, who have received the Holy Spirit just as we have?” 48 And he commanded them to be baptized in the name of Jesus Christ. Then they asked him to remain for some days. (Acts 10)
Christian Water Baptism
After the disciples were baptized with the Holy Spirit, they baptized believers. Most references are simply that people were "baptized" but there is an event specifically stating it was a water baptism:
34 And the eunuch said to Philip, “About whom, I ask you, does the prophet say this, about himself or about someone else?” 35 Then Philip opened his mouth, and beginning with this Scripture he told him the good news about Jesus. 36 And as they were going along the road they came to some water, and the eunuch said, “See, here is water! What prevents me from being baptized?” 38 And he commanded the chariot to stop, and they both went down into the water, Philip and the eunuch, and he baptized him. (Acts 8)
Given the historical background of John's water baptism, it is fair to say all baptisms performed by the disciples were water baptisms.
Late in Paul's work of establishing churches in Macedonia and Achea, there are two descriptions of disciples who knew only of John baptism:
24 Now a Jew named Apollos, a native of Alexandria, came to Ephesus. He was an eloquent man, competent in the Scriptures. 25 He had been instructed in the way of the Lord. And being fervent in spirit, he spoke and taught accurately the things concerning Jesus, though he knew only the baptism of John. 26 He began to speak boldly in the synagogue, but when Priscilla and Aquila heard him, they took him aside and explained to him the way of God more accurately. (Acts 18)
Apollos knew only of John's baptism and had the way of God explained more accurately. The text is silent as to whether Apollos actually was baptized by John or simply knew of it. Also nothing is said about Apollos being baptized, although there is reasonable to assume he was
The second involves Paul and twelve disciples:
1 And it happened that while Apollos was at Corinth, Paul passed through the inland country and came to Ephesus. There he found some disciples. 2 And he said to them, “Did you receive the Holy Spirit when you believed?” And they said, “No, we have not even heard that there is a Holy Spirit.” 3 And he said, “Into what then were you baptized?” They said, “Into John's baptism.” 4 And Paul said, “John baptized with the baptism of repentance, telling the people to believe in the one who was to come after him, that is, Jesus.” 5 On hearing this, they were baptized in the name of the Lord Jesus. (Acts 19)
These events take place around 50 AD, well after John's work. It is unclear whether "John's baptism" refers to the actual work of the Baptist or to a continuation of John's baptism of repentance. The point of the two events seems to be to show John's baptism which was necessary before the death and resurrection of Jesus, is now no longer necessary or even sufficient.
Jewish Ritual Washings
Since Hebrews is written to those considering a return to Judaism, it is possible the "doctrine" of baptisms is referring to the ritual washings of Judaism. The Hebrew term was mikveh:
The practice of mikveh was quite common in the second Temple period, as shown by the large number of references to this custom in the Talmud. The ritual immersion for healings and service continued as prescribed by the Torah. However, especially interesting is the practice of t'vilah for Gentile converts to Judaism.
In addition to formal ritual washings, there is archaeological evidence from this period which suggests the practice of ritual washings was widespread:
To sum up what we know about the use of the household mikveh in the first century based on the rabbinic texts and archaeological finds: the average size of the mikveh suggests that ritual bathing was ordinarily practiced individually (no more than one person would enter the installation at a time) and the location of mikva'ot within the basements of private dwellings suggests this purification was done regularly and whenever deemed necessary.
The doctrine of baptisms could be referring to both what to do and what not to do (or is no longer necessary). From the point of positive instruction for Christians there are two baptisms: water and with the Holy Spirit. From the point of negative instruction, there is the inefficacy of only John's baptism and/or the need or value of ritual washings.
Given the audience, it is likely both are in view. That is, a return to Judaism and ritual washings makes no sense if a person has been baptized in the name of Jesus and with the Holy Spirit:
13 For if the blood of goats and bulls, and the sprinkling of defiled persons with the ashes of a heifer, sanctify for the purification of the flesh, 14 how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God. (Hebrews 9)
19 Therefore, brothers, since we have confidence to enter the holy places by the blood of Jesus, 20 by the new and living way that he opened for us through the curtain, that is, through his flesh, 21 and since we have a great priest over the house of God, 22 let us draw near with a true heart in full assurance of faith, with our hearts sprinkled clean from an evil conscience and our bodies washed with pure water. (Hebrews 10)
- Barney Kasdan, God's Appointed Customs, Lederer Books, 1996, p. 113