As Phoebe notes there are many good resources for finding out about this. One of the primary sources is the Didache. The structure for the Liturgy in the Didache parallels pretty much exactly that given in Luke. After the Eucharistic meal and after everyone partook of the final cup of Christ's Blood, then the prophets would be invited to come and speak. This is similar to the practice in some Orthodox parishes to have the sermon after the service, instead of after the Gospel reading. There are strict guidelines given for how to judge and regulate the non-ordained prophets and teachers. Here is a link to the Didache see ch 10-13.
Anna, thank you for the reference.
It was not "impromptu" at all. It is exactly the tendency to become impromptu that St Paul is rebuking the Corinthians for and trying to correct.
What do you mean that these speeches of the prophets were not "impromptu"?
"Impromptu" means that something is unplanned, improvised or unrehearsed.
In this case, the Didache plans for the prophet's speech to be at the end of the service, and requires that the speech follows certain rules. For example, a traveling prophet is not supposed to just stay as a wanderer for more than 3 days and ask for a table to be made for him.
The fact that the moment for the speech is planned and that the speech must follow certain rules does not prevent this from being an improvised or impromptu speech, however. The prophet can still, unrehearsed, improvise and privately invent his content, so long as it doesn't contradict the Church.
This in the Didache by the way does not sound so different from what a priest does in his sermons. The difference I suppose is that the priest gives a talk to teach, but the prophet gives "prophecy", and in Corinth the lay people brought their own private psalms, visions, "tongues", etc., which is more individualistic.
Here is a link to a post I made earlier where you can see the parallel between Luke and the Didache, it makes pretty clear exactly what the structure of the service was. It is interesting to note that at this time the actual meal was sacramental - only the baptized could partake of that meal. A variant that we see come into practice later is that the meal is at the end.
Sure, as you said, the meal was sacramental. Sacraments and rites were part of the early Church and there was a structure and plan to it. It was not all informal and improvisational as some Charismatics claim.