Once you arrive at the destination town, enter it. You'll need to find the Guild Master. He is typically located in the town square or near the market area. Like the merchant, he will have a green exclamation mark above his head. Approach him and initiate a conversation. Select the dialogue option to deliver the letter.
Upon successful delivery, the Guild Master will thank you and provide a small monetary reward and some experience points. This completes 'The Merchant's Request'. He may also offer you another quest, which can be a good way to continue earning money and reputation in the early game. This quest serves as a basic introduction to the questing system and interacting with NPCs in towns.