How do you know if a gift has been sent?

If they sent a key, you get a blinking icon. The giveaway's creator has a week to send a gift/key.
Have they been online ehr since the giveaway ended?

Id wait for 3 more days, and then inquire in one of the old giveaways of the Gifter.

check notification on steam if its supposed to be a steam gift.
otherwise the icon will flash if its a key once the gifter sends it

If someone sends a gift there will always be an email, whether it is from humble or the steam store. I'd leave a comment on the giveaway page asking if they forgot. If it's on steam store you will have to be friends, did you ever send a friend request?

Start Here

There is some good info there and you've gotten some good advice, congrats on your first win :)

The key (or gift) is not sent automatically, the gifter has to log in and click a button to 'release' the key to you.
I think the rules state to allow for up to 7 days for you to receive the gift before marking it as 'not received'.

Once you do receive your key, please make sure to mark it as received!

Congrats and welcome to Steamgifts! =)