How you know you win???

A green bar appears telling you, that you won

A big green bar at the top of the site will tell you. You can't miss it.

ok thx

Hoorah for non-sarcastic answers.

Also click Giveaways at the top then View Won. If you won something It'd be there.

Another way is dependent on how the person gives you the gift, if they E-mail it you'll see it in your e-mail, if its gifted to you via the Steam Client the mail icon at the top-right next to your username should be green. If they add you as a friend the mail icon should also turn green.

Use the damn search on the forums next time ._.