how do i handle the gift code to the winner?

You have to send them an e-mail, or add them on Steam.

Email is usually provide beside the name of the winner, or you can add him on steam

Go here: http://www.steamgifts.com/manage/created, then click on "Send Gifts" or similar.

By the way, there's a guide in the forum.
It explain things nicely. I did use it when I did my first giveaway.

When someone wins a giveaway, its email address is shown to giveaway creator.

You simply send the gift/code to that email. That's the best, fastest and more secure way.

You can also add the winner on steam, but if you don't know what you're doing, you could get scammed.

No no no! This is how it works around here; usually people add me on Steam and give me the code where I continue to contact the winner and pass the code onto them.