First, you need to register an account. If you haven't already done so, click here.
Head over to the main seller search page and select how you want to be paid for your Litecoins.
You will see a table of all the applicable buyers, like the one below. Find one with your desired payment method and cost, and hit the sell button.
If you are selling for cash, make sure the seller is near you. You or they will have to travel for a meeting.
You will see all of your trade information, as well as a chat window to talk to the buyer. Say hi, make sure you agree on how payment will occur. At this point, you will send Litecoin to the escrow account. You can find the address in the status section, right above the cancel the trade button. It takes 8 blocks, or about 20 minutes, to confirm, so be patient. Once the transaction is completely funded, the buyer should send the money and click the mark payment complete button.
You need to calculate the risk when selling Litecoins via reversible payment methods online. Localbitcoins.com provide a guide for selling bitcoins online and it is recommended to take a look at it before you start selling Litecoins online.
The buyer should now have sent the money over your agreed method of payment, and marked the payment complete. Once you are sure that you have recieved the money, enter your password and release the Litecoins. Once released the trade is considered to be final and cannot be disputed.