"For thirteen hundred years was baptism an immersion of the person under water." - BRENNER
The earliest first century witnesses:
80 AD Hermas: "'I have heard, sir,' said I, 'from some teacher, that there is no other repentance except that which took place when we went down into the water and obtained the remission of our former sins.' He said to me, 'You have heard rightly, for so it is'"
The Shepherd 4:3:1
"The deacon raised his hand, and Publius Decius stepped through the baptistry door. Standing waist-deep in the pool was Marcus Vasca the woodseller. He was smiling as Publius waded into the pool beside him. ‘Credis?’ he asked. ‘Credo,’ responded Publius. ‘I believe that my salvation comes from Jesus the Christ, Who was crucified under Pontius Pilate. With Him I died that with Him I may have Eternal Life.’ Then he felt strong arms supporting him as he let himself fall backward into the pool, and heard Marcus’ voice in his ear ---- ‘I baptize you in the Name of the Lord Jesus’ ---- as the cold water closed over him."
Schaff-herzog Ency. of Religious Knowledge, Volume 1, page 435--1966 edition
Concerning the Didache:
Jonathan Draper writes (Gospel Perspectives, v. 5, p. 269):
Athanasius describes it as 'appointed by the Fathers to be read by those who newly join us, and who wish for instruction in the word of goodness' (Festal Letter 39:7).
Hence a date for the Didache in its present form later than the second century must be considered unlikely, and a date before the end of the first century probable.
Draper states in a footnote (ibid., p. 284), "A new consensus is emerging for a date c. 100 AD."
Stephen J. Patterson comments on the dating of the Didache (The Gospel of Thomas and Jesus, p. 173):
"Of course today, when the similarities between the Didache and Barnabas, or the Shepherd of Hermas, are no longer taken as proof that the Didache is literarily dependent upon these documents, the trend is to date the Didache much earlier, at least by the end of the first century or the beginning of the second, and in the case of Jean-P. Audet, as early as 50-70 C.E."
Stevan Davies comments on the Didache (Jesus the Healer, p. 175):
"The Didache is a text that gives instruction on how a Christian community should treat itinerant Christian prophets. It was written sometime in the late first or early second century and gives good evidence for a structured church's shift in orientation away from spirit-possession.
As for baptism in the first to third centuries:
'From writers of unquestionable authority, it is evident, that the primitive christians continued to baptize in rivers, pools, and baths, until about the middle of the 3rd century.
Justin Martyr says, that they went with the catechumens to a place where there was water, and Tertullian adds, that the candidates for baptism made a profession of faith twice, once in the church, and then again when they came to the water, and it was quite indifferent whether it were the sea, or a pool, a lake, or a river, or a bath. Such are the accounts given by Justin Martyr in his Apology, and by Tertullian on baptism as quoted by Robinson.
The sacrament of baptism, says Mosheim, was administered in the first century, without the public assemblies, in places appointed and prepared for that purpose, and was performed by immersion of the whole body in the baptismal fount.
Ecclesiastical History, Philadelphia edition, vol. 1. p. 126.
Justin Martyr is a second century witness. So is Tertullian (he lived in the second to the third century, for your information, and wrote throughout both of them). One of the quotes I provided from Tertullian was dated 198AD.
Here's another quote, to let you know which word he used:
Upon that, we are immersed (Latin: mergo, to dip, to immerse) three times, making a somewhat ampler pledge than the Lord has appointed in the gospel.
Then, when we are taken up, we tast first of all a mixture of milk and honey. Then, from that day, we refrain from the daily bath for a whole week.
Tertullian, c. 211, 3.94.
"Baptism itself is a corporal act by which we are plunged into the water, while its effect is spiritual, in that we are freed from our sins"
"`And (Naaman) dipped himself . . . seven times in the Jordan' (2 Kgs. 5:14). It was not for nothing that Naaman of old, when suffering from leprosy, was purified upon his being baptized, but (this served) as an indication to us. For as we are lepers in sin, we are made clean, by means of the sacred water and the invocation of the Lord, from our old transgressions, being spiritually regenerated as new-born babes, even as the Lord has declared: `Except a man be born again through water and the Spirit, he shall not enter into the kingdom of heaven'"
Justin Martyr made it clear that baptism required knowledge, an informed decision an infant could not make:
And this washing is called illumination, because they who learn these things are illuminated in their understandings. And in the name of Jesus Christ, who was crucified under Pontius Pilate, and in the name of the Holy Ghost, who through the prophets foretold all things about Jesus, he who is illuminated is washed.
Justin Martyr, First Apology of Justin Martyr, Chapter 61, Christian Baptism, Vol. 1
Then these fourth century witnesses:
Cyril of Jerusalem, 360:
For as he who plunges into the waters and is baptized is surrounded on all sides by the waters...
Basil of Casearea, 370:
How then do we become in the likeness of his death? We were buried with him through baptism....How then do we accomplish the descent into Hades?
We imitate the burial of Christ through baptism. For the bodies of those being baptized are as it were buried in water.
So therefore also in baptism, since it is a likeness of death, without doubt when you dip and rise up there is made a likeness of the resurrection.
375 AD Basil the Great:
This then is what it means to be `born again of water and Spirit': Just as our dying is effected in the water [Rom. 6:3, Col. 2:12-13], our living is wrought
through the Spirit. In three immersions and an equal number of invocations the great mystery of baptism is completed in such a way that the type of death may be shown figuratively, and that by the handing on of divine knowledge the souls of the baptized may be illuminated. If, therefore, there is any grace in the water, it is not from the nature of water, but from the Spirit's presence there.
The Holy Spirit, 15:35
381 AD Ambrose of Milan: "Although we are baptized with water and the Spirit, the latter is much superior to the former, and is not therefore to be separated from the Father and-the Son. There are, however, many who, because we are baptized with water and the Spirit, think that there is no difference in the offices of water and the Spirit, and therefore think that they do not differ in nature. Nor do they observe that we are buried in the element of water that we may rise again renewed by the Spirit.
The Holy Spirit 1:6[75-76]
John Chrysostom, 390:
Exactly as in some tomb, when we sink our heads in water, the old man is buried, and as he is submerged below, he is absolutely and entirely hidden...