I've never looked into LocalBitcoins, can anybody let me know if this assessment from a Reddit user is correct? "1) Someone makes an offer to buy your bitcoins 2) You send the bitcoins to localbitcoins 3) When you get the cash, you send a text message to localbitcoins, the bitcoins are instantly transferred". I found 1 person looking to buy in my city.
That's basically how it works, but you contact the buyer in your case unless you plan to sell regularly.
You should send the bitcoins to your LocalBitcoins wallet ahead of time so that you don't have to wait for them to be confirmed. Alternatively, you can just send the bitcoins directly to the buyer's wallet. In this case, the buyer might want to wait for a confirmation, though.