A large and not entirely coherent subject, with very patchy evidence. So this contains much discussion of the incoherency and the difficulty in reconstruction.
The practice of worshipping the gods according to the customs of your forefathers and not troubling your head about the customs of your neighbors if you, or they, are immigrants and consequently differ. The importance of antiquity -- Christians argued that Moses predated the Iliad because that was a strong debating point. The spill-over to the practices of others -- magistrates and emperors would pay courtesy calls on the local gods. Though immigration does seem to be the overwhelming cause of the worship of foreign gods -- and the evidence may be underplaying it, because an Italian father and an Egyptian mother could result in a child with an Italian name raising an inscription to Isis as an ancestral religion though you could not tell.
The habit of stringing together names of gods as one. Gods were actually saluted as polyonymous -- many named -- and you can work out what some inscriptions were about by the titles applied. Many gods were addressed as Healer about the cure of diseases and injuries.
How mysterious the mysteries weren't. Not only do the account tell of the initiations happening in public at temples open to the general population, we have an account where a man is derided as being the only person in Athens not initiated into the Eleusinian mysteries.
Dreams were a common way to discover the will of the gods, and oracles after them. Many inscriptions recount that "I was commanded" before recounting a sacrifice, so many that it was abbreviated. We not only have inscriptions raised to one god by people who described themselves as the priest of another, but some where the person said that he did this sacrifice, made this dedication, etc. to one god at the command of another.
Feasts were a big deal. Shrines had kitchens and dining rooms that were larger than anyone but the extremely rich could afford, and people would have their banquets there, with invitations saying it would be "at the couch of Serapis."
Considerations of the afterlife were -- not large, actually. Initiations were thrown in as things that religions gave you, but not that they promised great wonders for the afterlife. Putting that you had been annihilated and did not care on your tombstone was so prevalent that they abbreviated it.
There were philosophers who criticized elements. For instance, one scornfully declared that everything the Christians said about the falsity of idols was repeating what a philosopher had said before them.