How do you prove a culture is pure colony bacteria?

A colony is one 'circle' of bacteria, to distinguish between them you could try testing them with antibiotics, increasing/lowering temperature, increasing/lowering humidity (or pH), changing the components of their nutrients (blood agar, starch agar etc) or even changing the atmosphere they are in (so removal of oxygen, addition of nitrogen/carbon dioxide). You can separate each colony by determining what conditions each bacteria work best in, simply by changing a few factors, then attempting to regrow them. Also there are several staining methods which you could try, gram staining, simple iodine tests, which could also differentiate each colony.