Thieves Guild
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 Grey Fox". After reading one of those posters, you'll have a new conversation topic for The Grey 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 deacreases. 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 a 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 others 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.
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, 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. She's not going to take it back to Armand immediately, so you've got a day in which to get it from her. Remember, killing her is not an option. 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.
Independent Thievery
Now that you're in the Guild, you're pretty much on your own. Your quest is called "Independent Thievery" and its whole objective is to break into people's houses, steal their stuff and sell it to your fence. At this time it's Ongar in Bruma - he lives in the little shack behind the chapel, but spends most of his day drinking with his buddies at Olav's or wandering the streets.
I found a quick way to deal with all of the fencing in just about one fell swoop. As part of the Main Quest, after you break the Siege at Kvatch and take Martin to Jauffre, you go to Cloud Ruler Temple near Bruma (what a coincidence). If you have no bounty at the time, Jauffre will ask you to join the Blades. If you have a bounty, no matter how small, he will not make the offer. This is crucial because if you are a member of the Blades, you can't steal the stuff from Cloud Ruler (as a member of the faction, you can take what you want with no penalty). You can always decline the offer for now and join later. Anyway, there is a ton of stuff in the west wing of the Temple. During the day, there is only one guard in that part of the temple and he doesn't care if you close doors so that he can't see what you're doing. So just close the door, drop into Stealth mode, take everything that has a value (and there's a lot of it, including an unlocked jewelry box) and then saunter right down to Bruma and sell the stuff to Ongar. And even if you steal all of the Akaviri Katanas in the Temple, they'll give you another one when you join the Blades. All told, you should be able to fence close to a thousand septims' worth off of that one haul.
Some users have reported a problem with the final quest for the Thieves Guild that may trace its way back to this Independent Thievery mission. It appears that fencing significantly more than the required amount at your current rank can cause some script triggers to not set correctly, which breaks the last mission. At the time of this writing, I have not worked my way through all of the Thieves Guild missions, so I can neither confirm nor deny that this is the case, but be aware that others have reported this problem. Best advice: fence what you need to fence, but cut it off at about 1000 septims.
Update: in the problem of triggers not setting correctly, player impatience may be contributing to the problem, too. If you have fenced the appropriate amount of loot, wait for the Journal updates after completing each mission. There are two of them: one tells you how much you need to fence before you can get another mission and the other one tells you that you have reached that goal. If you don't wait for the second Journal update, you might be messing up the questline triggers. Patience and fortitude. The wait between updates is only a couple of seconds (real time).