In Diablo 3 for the PC, items that you win in the Auction House don’t go straight to your character or your stash, they go to a holding spot in the Auction House until you claim them.
In order to claim your won items from the Auction House, you just need to open up the Auction House and go to the Completed tab at the top.
On the left hand side, you’ll see all of the auctions you successfully won that haven’t been claimed. This is the same place you’ll collect money from items you’ve sold as well, and items that didn’t sell go here too.
Highlight the item you want, and click the “Send to Stash” button. As long as you have space in your current character’s stash, then that’s where they’ll go.
Make sure you’re logged into the right character obviously before you do this.