I've used coinbase and it takes awhile but has low fees and is based in the US so I trust it.
How do you transfer bitcoins from your wallet to your coinbase account in order to sell them?
You'll have to look up an address associated with your Coinbase account. You can find this under Account Settings->Integrations, toward the bottom of the page.
Copy an existing address, or create a new one. In Bitcoin-Qt, go to the Send coins tab, and paste in the address you got from Coinbase. I like to send a smaller amount first just to test for any painful copy-and-paste errors, then send the rest when the smaller amount goes through.