To join the thieves guild, you will have to find a thief guildmaster. The most commonly used thief guildmaster is named Vandoren, located south of the west Britain bank. To join, simply say the guildmaster's name followed by "join" while standing near it. In the case of Vandoren, say "Vandoren join".
When you meet the requirements (see the related questions for details), the thief guildmaster will ask you for a small fee of 500 gold. Simply drag and drop 500 gold pieces on the thief guild master, and you will be a member of the guild.