I just attended a republican caucus last night. I cant comment on primaries as ive never experienced one.
I first registered as republican so I was able to attend, then went to my precinct. Precincts are just based on geographic areas. A town is often split into many precincts. You should see lots of familiar faces since your neighbors will b there as well. We had to listen to each candidates representative, if there is one. This took less than a hr. We then picked representatives for our precinct, which seemed like they were chosen ahead of time, but thats to just speed up the process. We then vote, and your encouraged to come back for results and other rebublican things that many people choose skip out on. I took me 2 hrs from registation to voting.