The little ball is the polina. You toss that out first. Then you see how close you can get your other balls to it. Most of the sets you get at WallyWorld and such come with 4 different colors for 4 teams. Official sets tend to have just 4 red and 4 green balls.
Bocce is referred to as lawn bowling, is really played on a "court" of clay. The court is normally around 6ft wide by a good 20ft long. There are side rails and back stops at both ends. You can play your balls off the backstop. About 3ft short of each backstop is a line. The Polina must not cross the line. If your Bocce ball crosses the line and stays there, it's not counted in the points even if it's the ball closest to the polina.
It's an old game from Sicily. I'm trying to remember which movie the is a short clip of them playing it. Probably a GodFather movie, lol Back home we have a very large Sicilian/Italian population. Years back a few of the parks had Bocce ball courts. It can be as competative as folks do with shuffleboard!