Early Christianity was only tenuously a religion- rather, one much more like talkative, passionate, and quarrelsome social circles. They lacked shrines, temples, statues, sacrifices, public festivals, dances, music, pilgrimages, and even inscriptions.
Yet they did have rituals, symbolic action representing what the society deems important- and without which, indeed, a society may not be possible, as social relationships require symbolic acts.
The two rituals which Christianity obviously had were, of course, baptism and the Lord's supper. But they also met regularly, which itself becomes a ritual- weekly and on Sundays, as it happens.
What happened at these meetings? Chanting and singing, as evidenced by Paul's periodic hymns and psalms. It is also likely, though not certain, that assemblies read from Scripture; we also know that some preached by making proclamations, and others taught. We might also assume that exhortations of the sort found in the Epistles were also common in conversation there.
The only thing special about these rituals was their blend of the familiar and the novel- an outsider would have recognized all of these things, but also would have thought their combination and application altogether strange.
But these numinous rituals accomplished three key things: they increased feelings of solidarity, upped the prestige of individuals, and marked the occasion as solemn.
Baptism, of course, was a more solemn ritual than most, miming Christ's death and resurrection. These were most likely full immersions in water, with the baptized performing the rite naked- likely in a river, or, failing that opportunity, with a tub and a bowl. The baptized took off and put on clothing to signify the "old man" and the "new human". They might also have shouted out Abba to signify their new intimacy with God as heavenly father.
The Eucharist was a rather more subtly symbolic affair. It likely alluded to the festival meals common in all voluntary associations- especially with those of the burial clubs that commemorated the deaths and interment of their members. They included the saying of Christ, "this is my body" and "this is my blood" as ritual pronouncements.
And just as in those burial clubs, the wealthy members likely hosted these meals for everyone, as patrons- this eventually led to disputes. But this could not be, precisely because of the nature of the ritual: all the members were one body, the body of Christ. They were sharing a holy meal within a sacred world of symbols; this dissolved the boundary between rich and poor as much as it dismantled the boundary between Gentile and Jew.
And no, no one still knows what the baptism for the dead was all about. Sorry.