Wow, starting out with public giveaways. That's a place I still haven't gone to yet.
And adding onto what Darko said, don't prematurely send an email to the winner with the code after the GA ends and you're told who the winner is. Many GOGers will admit they've been burned by doing that with people they don't know - whether publicly or even within the group here.
Send a friend request first thru Steam. (You can always remove them later). This serves a couple purposes - one, if their profile is private, friending them should make it viewable so you can verify they don't already have the game. Two, I find it easier to pass a code via Steam chat which is possible after friending. One of my most recent giveaways, the winner would not even have his profile visible to friends so after a week of trying to get him to let me view it so I could verify he didn't have the game, I asked for and was allowed a reroll. He never responded to me after accepting my friend request thru chat so I can imagine how dismissive he'd have been via email.
But if you can verify they don't have the game, the rest should be easy. If the game is in your Steam inventory, just pass it on to them thru the inventory system. If you have a key, again I find it best to open a chat window with them and give them the key that way as opposed to email. And then before saying bye, kindly remind them to mark the game as received on SG so you don't get a black mark should they forget to do that. And then a day or so after the GA ends, I go check their profile again to make sure they did activate the key and it is now in their library. Only twice has someone not activated their won keys from me and in that case, I notify SG mods after 7 days and they take care of it.
Hopefully, it goes smooth for you but if not, there's a whole thread here to ask questions. Good luck.