What happens when you get off the plane in Rome?

Yes, passport control and customs are two different checkpoints but you simply follow the signs and that's it. Passport check is before you pick up checked luggage, custom is after you have your checked luggage. It's hard to predict how long the process will take as it depends on how busy the airport is. But it really shouldn't take 3 hours, one hour total is much more likely.

Your concern is quite understandable but things are probably going to go much easier and quicker than you think. You get off the plane follow the signs to the tram/monorail which will take you down to the baggage claim. You get your bags then follow the signs to the passport booth and they stamp you in. I remember then I simply went to the exit where there was a small station for you to [INVALID] for customs. But no official called me over or checked me for anything and I just walked out....total time maybe 1 hour...if that. My hotel had transportation waiting for me and off I went. Everything I worked myself up for in the negative sense never happened. I would worry more about getting away from the airport than going through. Have fun....Italy is great.

For my post above....replace the word INVALID....with the word 'declare'...not sure why it did that and it wouldn't edit

Beatrix is correct, you go through passport control first and then pick up your luggage. Use the Nothing to Declare line to exit after picking up luggage (unless of course you have something to declare) and you'll probably zip right through customs. Unless luggage is slow to arrive at the carousel, you should be on your way in under an hour. Once you exit, it's just a short walk to the taxis and an easy 5+ minute walk to the train. There are ATMs along the way to the train.

JULIA, based on my experience a few months ago, your transit through FCO MAY be quick or it MAY be delayed somewhat. Depending on the number of flights that are arriving at the same time, the trip through Passport Control should be fairly quick. They will stamp your Passport, since this is your first point of entry into the E.U. Customs shouldn't be a concern since you likely won't be transporting anything expect personal belongings. However, the baggage claim part could be interesting. In the past I've had no problems with arrival in Rome, but for some reason this year was different (hopefully just a temporary situation). After waiting for over 30 minutes for the luggage to appear, I finally asked an official. It turned out that the luggage for the flight I arrived on had been diverted to another terminal. That meant a walk, another queue and GOING THROUGH SECURITY again just to collect my bag! The process took the better part of two hours and was a darn nuisance! Were you planning to use the Leonardo Express to get into Rome? If so, when you've collected your luggage follow the signs to the rail station. When you arrive there you'll see the two tracks, one of which will probably have a train waiting. Buy your tickets (€14 PP from the machine or €15 from the ticket booth as I recall). AFAIK you'll be able to use a magnetic strip credit cards in the ticket machines. DON'T FORGET to validate the tickets in the yellow box at the end of the tracks! It will probably seem a bit chaotic, especially as it's your first time in Europe. Rome tends to be a bit of a "culture shock" for first time travellers to Europe. If possible, I'd suggest pre-reading "Europe Through The Back Door" before you leave, especially the "Rail Skills" chapter. Be sure to wear a Money Belt! When will you be arriving in Rome? Happy travels!

If at all possible, try to convince your travel mates to use carry on luggage. Eliminate the claiming baggage headache.

Yes, simply follow the crowd through passport control and customs. It's virtually impossible to get lost. If you're carry on, you can then head directly into town instead of waiting for your luggage (and possibly having to fill out forms for your lost luggage). We used the train from the airport (two airports though, only one served by train).