How to move bitcoins from an exchange into my wallet? Completely new to this. Bought some Bitcoins from Bitcoin.de and received confirmation that the trade has been completed and they show me my balance.

Downloaded a wallet from Bitcoin-QT. That's fine. Now, how do I get the Bitcoins I've bought into the wallet I've downloaded? And how do I then use them to buy something online?
First thing, encrypt the wallet with a good passphrase.

You will want to go to the receive tab in Bitcoin-QT,  and create a new receiving address for yourself. You may want to create a new address for every transaction for anonymity purposes. Copy the address to your clipboard and then go to bitcoin.de, and send the coins from your account to that address.  It may take an hour or so for the transaction to complete so just leave the client running and be patient.

HINT: Be sure that bitcoin-qt is finished syncing with the blockchain before you send yourself the coins or you may not be able to accesss your coins  for the 24-48+ hours this process can initially take!  If you need it faster, might want to temporarily use either electrum or blockchain.info wallet until the client is completely synced.