Nights in Rimini are great... but the biggest clubs are right outside of the main city in the hills surrounding the town, in order to get there the almost only solution would be to grab a taxi. With hundreds of people trying to taxi themselves to the hills after dinner, this could be quite "fun"! The best option if you are downtown would be to go to Central Station and grab a taxi from there, there will certainly be others going your same way and if you are not shy you will get a lift to the hills in a shared taxi.
If you are staying at one of the hotels in the seaside strip you can get a taxi from there (the hotel will arrange for your cab to pick you up without problems)
Coming back home will also be a challenge but it should not be that much of a problem for the skilled party-goer. Clubs close at about 7/8 AM (only to reopen as matinnées or after hours an hour later). By the time you come out of the clubs there will be a bus line already in service so... not to worry (be careful with late Sunday starts for buses, you might have to ask for a ride home -thousands of people head back to the beach at the same time and it should not be too hard to find someone going your way)
