Lets say you bought 0.5 bitcoin from Coinbase. You may have to wait a few days until they deposit to your account. Once that happens, you can either leave the money in your account or transfer it.
When you click on "Send Money" the following appears:
For example, here is a screenshot from BTC-E.com.
You simply copy the deposit address from BTC-E and paste it in the "send money to" field at Coinbase. Once you do this the funds will transfer. It could take an hour (or longer) for the funds to be confirmed. If you make a mistake and transfer the funds to the wrong address, you will not be able to access the money and you can not reverse the transaction. Be careful.