You can tell a lot from a rodent's behaviour. Your hamster should be lively, active, aware, chewing on anything it can get its teeth on, climbing up the bars and so on. As well as this, he should have glossy fur, pricked up ears and bright eyes. All these things show that your hamster is happy and healthy.
Of course, not all of these factors have to be present; hamsters have their own personalities, too, don't forget, so don't worry if, after reading this, you think, "Oh no! But he always moves around slowly!" or "But my hamster doesn't like to chew on things at all!" (if so, count yourself lucky!) - one of my mice used to be like this but it was just the way he was!
I hope this helps. Enjoy your new pet! :)