I'm actually on holiday and I have won a giveaway

Contact the creator of the giveaway, explain to him and see if he's okay to wait until you're back.

Whatever you do, don't mark it as received beforehand.

Or... if there's somebody you can really trust with your password (family, close friend), maybe ask him to redeem on your account ?

if it's an expensive game, you could even go to an internet café and activate it that way.

if you are in a hotel, doesn't it have a pc/laptop for their clients?

just assuming you aren't camping or something like that :3

Remote control?
both chrome, or teamviewer. take control of your home computer.

When will you be back ? You have 7 days to activate your game

Maybe some relative at home you trust your account with to activate the game for you?
Or if it's not a big game, then I would just ask the host to re-roll, good karma for the next GA :p

Ask for a reroll, stop entering giveaways and enjoy your holiday.

Just like DavidSarif said,

Contact the creator of the giveaway, explain to him and see if he's okay to wait until you're back.

Yup, contact the creator and request a re-roll, if it's a game you really want find a way to activate it before the 7 days pass.

Also although it is unlikely you win another one you should probably pull all your entries.

write to the steam support to activate the gamekey on your steam account, check the activation there and mark the win as recived.