Yeah when the giveaway is over you will see the name of the winner in the Giveaways>View Created. You just go to there steam profile and add them on steam. You can trade it to them from there.

Just make sure this is a game in you inventory and not a redeemed game that you own (ie can instal and play)

Hope that helps.

When the GA ends, you will see a red box when you visit the site. There will be a link there. When you follow the link, you will see who won the GA. You can also see their email address. If you visit the winner's profile, you will also see a link to their Steam profile.

So you have two choices. Either send a friend request in Steam so that you can then open a trade window, or try to contact the person first through email. Since this this a steam gift rather than a steam serial key, you probably want to go the first route (add the winner on steam as a friend and then trade the gift there.)

Once you traded the gift, you then tick the "gift sent" checkbox. The person who received the gift must then also check the "I received this gift" checkbox on their end. Make sure to remind them to do that; sometimes they forget. It's important that they do this, otherwise you get a bad reputation, since it would appear that you didn't send anything.

Hope that helps :)