American roulette is a slightly faster game. There is a smaller number of players and they generally place their own chips on the table. American chips are predominantly used. Just ask the croupier for a colour that is still available. You decide the value of your colour yourself and the croupier will place a chip on top of a rail near the wheel, and then places a marker on top of that to indicate the value of that colour chip for that session.
If you want to end your game and leave the table, you must first ask the croupier to exchange your American chips for value chips, because your American chips are only valid at the table where the value of your colour is marked.