How can i claim my gift after i win the giveaway?

Add the person on steam/the person on steam will add you. Or...the person will email you the key or something like that.

With e-mail or via Steam trade.

The giveaway creator will try to contact you, either through e-mail or Steam. ;)

Thanks! :D

it depends on the description of the giveaway. if there is no description wait a while to contact the creator (usually 24h)
if the description says he'll add you just wait till he does and if he forgets or seems to be, add him on steam
as for keys, they usually send them via email.
and when that's done, click on the green banner and tick the "I've received the gift" box.
before ticking the "i haven't received the gift" box wait at least a week to give the creator the opportunity to contact you

You can't