1) Be prepared to walk everywhere in Rome (and bring good walking shoes). Places are in close distance to each other which makes it easier for the traveler. Use the metro or bus for further distances as it will save you time and even money, for example, the Vatican is a quite a distance from the Colosseum.
2) To cross the street, you might be used to pressing the button which stops traffic one way. It’s actually common on smaller streets without traffic lights for people just to cross or jaywalk when there’s a clear opportunity. Usually, cars will stop for you when crossing. Just be careful!
3) Most of the time public bathrooms do not have toilet seats. Some places also charge you to use the washroom or do not have free toilet paper. Again be prepared with small tissues in your bag.
4) When visiting famous monuments such as the Colosseum many street vendors will approach you trying to sell souvenirs. One time over 10 different people came up to me selling either a selfie stick or scarfs.
5) Learn a least a few common phrases such as “Ciao” or “Grazie” they go a long way. Fortunately, most people know some English in the city so it’s easy to communicate.
6) Rome is a busy city, as a matter of fact it’s the busiest in all of Italy. Everything from the metro to the churches is crowded so if you can plan visits in the early morning or evening.