The Thieves Guild is back to being a secret society, so your first order of business is to figure out how to find them. Oh, you'll find lots of people who can talk to you about the Thieves Guild, but no one who can give you any concrete information. That is *until* you do something to bring yourself to the attention of the Guild. There are two ways to do this: the simple way and the not-so-simple way.
The simple way: scattered around the Imperial City are wanted posters for a fellow called "The Gray Fox". After reading one of those posters, you'll have a new conversation topic for The Gray Fox. No one can tell you much until you ask a beggar whose disposition is 70 or better. At that point, they'll ask whether you want to find him. If you answer that you want to work with him, you'll be told to go to the Garden of Dareloth in the Waterfront district at midnight.
The not-so-simple way is to get thrown in jail. Make sure it's for something simple and cheap, like stealing an apple, because you have to serve your sentence and long sentences can mean large skill decreases. If you'd like to kill two birds with one stone, as it were, there is a Miscellaneous Quest ("Two Sides of the Coin" - available in Bruma) where you have to get thrown in jail to progress the questline, anyway. So activate that quest, steal a cheap item of some kind, and move both quests forward with one stint in the slammer.
After you are released from jail, you'll be contacted and receive a "Mysterious Note" telling you to come to the Garden of Dareloth on the Waterfront district at midnight. If you are in the Imperial City when you do your time, you should get the note fairly quickly (a few hours, maybe). If you are in another town, it will take longer (a day or two). And if you hop around from town to town, it may take quite a while before the messenger catches up with you.
Of course, if you really want to cheat, just go there directly. Christophe won't have anything to say to you until you've either gotten the information from a beggar or through the Mysterious Note, but all three of the NPCs are there starting at midnight every night (some people just have no life).
Seems like a lot of people have problems finding this Garden of Dareloth (compasses are wonderful things - hint, hint). So if you must be well-and-truly spoiled, find the boarded up storefront in the Waterfront District. The Garden will be directly behind the building at that point. It's the little walled area between the main building and the Abandoned Shack. At midnight, Armand Christophe and two other potential guild members (Amusei and Methredhel) will come to the Garden. Armand proposes a little contest to decide which of you gets to join the Guild - whoever can steal the diary of Amantius Allectus (without killing him) and bring it back can join the guild. And no killing each other, either - this isn't the Dark Brotherhood, after all.
If you want to do this legitimately, roust the beggar just outside of the walled area and bribe his disposition up until he tells you where Allectus lives. If you've pretty thoroughly canvassed the Imperial City, his house will already be on your map and you just need to know which district. Make sure you take some lockpicks (Armand can sell them to you for 5 gold each) because the front door is going to be locked. It's a two-pin lock, so you shouldn't need too many. Now go and steal the diary and bring it back to Armand.
Amusei is not going to be much of a competitor (you'll be seeing quite a bit of him in other quests after you join the Guild), but Methredhel will be. She knows exactly where she's going, exactly where the diary is in the house, and she's probably faster than you (at least at the beginning of the game), so it's going to be a real race. If you want to be completely spoiled, Allectus lives in the Temple District and the diary is in the desk in the front room. The question is whether you're going to be able to get to it before Methredhel. Let's assume that you do. If you can get the diary first, take it back to Armand (he's probably still in the Garden) and you're in.
Now, let's assume that Methredhel gets the diary (which she probably will). She's not going to take it back to Armand immediately, so you've got about a day in which to get it from her. Remember, killing her is not an option, but stealing from her is. You're not in the Guild yet, so stealing from a fellow thief is perfectly OK. She lives in one of the shacks in the Waterfront district, so all you have to do is break in and steal it back. Fortunately, she and her roommate go out to dinner around 6-ish each day, so you should have ample opportunity to liberate it and give it to Armand when he shows up in the Garden again at midnight. Methredhel is a good sport about it, too, and will welcome you as a brother thief.
Now lets assume that you don't manage to retrieve the diary from Methredhel before she turns it over to Christophe. All is not lost. Wait a couple of days and talk to him again. He'll have a different mission for you. It's a bit more difficult than stealing the diary, but you're not really in a race (OK, it's a race against Amusei, but is it really a race if he can't win?). Steal a sword from Rohssan at "A Fighting Chance." The reason it's a bit more difficult is twofold.
First, you have to do it during a time when the store is closed. Merchants have a nasty habit of following you around so they can keep an eye on you, which makes breaking into the living area highly problematic during business hours. So you either have to do it when she's not there (like immediately after the store closes and she goes for dinner) or you have to do it when she's asleep, between midnight and 6.
The second problem is her pooch, who will start barking if he detects you. This will probably wake her up and she'll either spot you (fight-or-flight time) or kill the dog (Radiant AI has been known to cause some "interesting" behaviors when pets do things their owners don't like). Perhaps both, depending on how annoyed she is with the dog. I'd put my money on her spotting you, though.
So, assuming you can break in at an appropriate time and avoid being spotted by either Rohssan or her dog, turn right when you enter and there will be a little nook ahead. Rohssan's chest is on a table in the nook. It's locked (like you were execting anything else) and the difficulty is going to depend on your level and security skill (the higher they are, the harder the lock is). Snag the sword, get out and report back to Armand.
On thing that you're going to have to keep an eye on is your Infamy. You'll hopefully have noticed that your gained one point of Infamy as soon as you joined the Thieves Guild. It's only going to get worse as you progress through the missions. In and of itself, your Infamy isn't that big of a deal. However, if it's higher than your Fame, you will not be able to get healing at the Chapels. So, while it's possible to just proceed through the questline, you'll probably want to break off and complete a side-quest or two or complete missions for the Mages Guild or Fighters Guild between gigs for the Thieves Guild. I didn't keep track of which missions did what to my Infamy, but I ended up with 29 points of Infamy by the end of the questline, was never detected in any of the missions and did no side quests or freelance dungeon-delving at all. There are a couple of other alternatives available to you, if you'd prefer.
Each Oblivion Gate that you close raises your Fame by 1 point. However those Gates don't start appearing until after you've got Martin safely ensconced at Cloud Ruler Temple. So you'll need to advance the Main Quest at least that far to take advantage of those Fame points. Additionally, each fight that you win at the Arena adds one Fame point. So you might want to work the Thieves Guild and Arena at the same time - do a job, win a fight; repeat.
Now for the fun stuff. One of the main threads running through the Thieves Guild quest line is "just who is this Gray Fox fellow, anyway?" If you are paying attention, you can pick up bits and pieces of the puzzle from reading things and by asking questions of appropriate people at appropriate times. At this point in your career, you can pick up the following information from conversations with your fellow guild members.