I bought some bitcoins from Bittylicious a few days ago. I didn't have a wallet at the time but Bitcoin Core wallet has finally synchronized. I have the transaction ID and address and everything I thought I needed, but I'm not sure where to find the private key. How do I spend these bitcoins? Any help is appreciated.
I didn't have a wallet at the time...
Do you mean your wallet just wasn't fully synced? You'll need some sort of a wallet to receive coins, regardless of whether it's fully synced or not.
I'm not sure where to find the private key
The GUI handles the management of private keys for you, so you don't really have to think about this if you don't want to. To send coins, all you need to do is go to the send coins tab and fill out the form.
(If did really need to get access to the private key, you can use the Debug Console (from help menu) and do
The only way to receive or spend bitcoins is to either have an online wallet or a private key with Bitcoin-qt wallet on your computer. If you for some reasen bought these bitcoins and gave the wrong key (mistyped or so) then you made someone very happy but it is not possible to make the transaction undone.