The mode of baptism
Whether baptism is immersion, pouring, or sprinkling, and what the terms and settings support.
Acts 8:36-38
36As they went on the way, they came to some water, and the eunuch said, “Behold, here is water. What is keeping me from being baptized?”
Verse 37 — the World English Bible omits this verse; the numbered slot is kept empty rather than filled from another edition.
38He commanded the chariot to stand still, and they both went down into the water, both Philip and the eunuch, and he baptized him.
What each tradition says
Rabbinic / Midrashic
The Rabbis connect the duty of bathing by complete immersion, tebilah, to the initiatory rites. Because sprinkling with blood was always accompanied by immersion, tradition connects this immersion with the blood lustration that also took place immediately before the Revelation. These three acts the source says were always performed upon proselytes to bring them under the wings of the Shekinah.
Kaufmann Kohler, Samuel Krauss, Baptism (Jewish Encyclopedia, 1901-1906) — Opening section (immersion in the initiatory rites)
Patristic
The Didache says that if there is no living water, baptize into other water. If cold is not possible, use warm; if neither is available, pour out water three times upon the head in the name of Father and Son and Holy Spirit.
The Didache (anon., 1st-2nd c.), The Didache (The Teaching of the Twelve Apostles) — Chapter 7 (Concerning Baptism)
Catholic
William Fanning states that three forms of ablution have prevailed among Christians: immersion, infusion, and aspersion. The Church holds all three valid because they fulfill the requisite signification of the baptismal laving. The most ancient form usually employed was unquestionably immersion.
William Fanning, Baptism (The Catholic Encyclopedia, 1907) — Section on the matter and the forms of baptism (immersion, infusion, aspersion)
Orthodox
Philaret of Moscow states that what is most essential in the administration of Baptism is trine immersion in water, in the name of the Father, and of the Son, and of the Holy Ghost. He gives this trine immersion, in that name, as the essential element of administering Baptism.
Philaret of Moscow (R. W. Blackmore trans.), The Longer Catechism of the Orthodox, Catholic, Eastern Church — Part II, On the Seventh Article of the Creed (Baptism), Q. 290
Reformed / Protestant
The Westminster Confession says that dipping a person into water is not necessary. It holds that baptism is rightly administered by pouring or sprinkling water upon the person.
Westminster Assembly (1646), The Creeds of Christendom, Vol. III (Philip Schaff) — The Westminster Confession of Faith — Chapter XXVIII (Of Baptism), section III
Evangelical
Albert Barnes writes that there might be various ways of baptizing, even after they were in the water, besides immersing. He adds that sprinkling or pouring might be performed there as well as elsewhere.
Albert Barnes, Albert Barnes' Bible Commentary, on Acts 8:38 — Notes on Acts 8:38 (the eunuch's baptism)