Chatting to him will kick off the 'A Chance Arrangement' quest. If you encounter him at night in the inn, he'll only redirect you to find him in the marketplace in the day, however. He can be found in the marketplace area in the daytime (8am-8pm) and in The Bee and Barb inn at night. Here's how to get in touch with the Thieves Guild in Skyrim: How to join The Thieves Guild
In order to join them you'll need to know who to speak to and track them down in order to get the introductions you need. Much as with The Dark Brotherhood, the thing about the Thieves Guild is they are by their very nature rather secretive. If you're playing Skyrim on Switch and like the idea of stealing things while on the go, this is the guild for you. If sneaking and taking down enemies quietly if at all is your sort of thing, The Thieves Guild is likely one of your top choices for a job in the world of Skyrim.
