The missions that are given to you by the thieves guild obviously require high Sneak and Security abilities. In most of them you are supposed to avoid combat, as any unnecessary casualties result in gold penalties from the guild itself.
Except for completing mission after mission, you also have to 'fence' a certain amount of money in order to be assigned some new special tasks. You fence money by stealing goods and selling them to special guild member known as, well, fences. That's the only way to earn money on stolen goods in Oblivion. See the quest "Independent Thievery" for details.
Required amount of fenced money:
May the Best Thief Win
Untaxing the Poor
The Elven Maiden
Taking Care of Lex
Arrow of Extrication
The Ultimate Heist
Finding the Thieves Guild
After some time spent in Cyrodiil, you'll surely notice Wanted posters in all bigger cities, pointing out the mysterious character of Gray Fox. He's presumed to be the Thieves Guild leader. You'll hear a gossip that the beggars are his eyes and ears. Question one of them (at least 2 of them are in every city), and raise his Disposition. You'll know that in order to join the Guild you are to be in the Garden of Daleroth in Imperial City Waterfront exactly at midnight. When you're there (there's a map marker for you), you'll meet Armand Christophe, together with two other guild-wannabes.
HINT: Armand won't talk 'business' with you in any other time or place, each time you want to report after performing a quest you have to wait until midnight and go to Garden of Daleroth.
HINT: A shorter way to find the Thieves Guild is to actually let city guard arrest you. When you have spent some time in jail, you'll be approached by a guild's messenger who'll tell you about the meeting place.
May the Best Thief Win
Your first task is to race the other two candidates in finding a man named Amentius Allectus and stealing his journal. Ask any beggar in the city about Amentius and you'll know that he lives in the Temple District. You'll find his house following the map marker. Picklock the door and steal the journal from the house - piece of cake. Armand will be satisfied with your performance and will gladly make you a guild member.
This mission follows you throughout your whole career as a Fighters Guild cooperative. To make things short, it's all about stealing and selling what you steal. The higher your rank, the more fences you'll be allowed to contact. All of them have a very high Mercantile ability, so cope with the fact that you probably won't be pulling any good bargains on them. After each quest you are informed how much money you need to fence before the next one becomes available.
The stolen goods are marked with a red hand in your inventory. You can't sell them in ordinary shops. Where do you get them? Well, you steal, of course. Steal from houses and pockets of every possible NPC in Cyrodiil. Sneak and Security are a must here.
Ongar the World-Weary
Imperial City, Elven Gardens
Untaxing the Poor
You have to take back the taxes that have been collected by the city guard from the Waterfront's people. They are being kept in South Watch Tower (access through Temple District or Arboretum). Climb the ladder up three times, using the lockpick the third time. The money and a tax record are in a closet to the right. Take them all and go back to Christophe. He says you can keep the money.
The Elven Maiden
Go to Cheydinhal. Talk to one of the beggars, paying him for some information. You'll know that the statue you are looking for is in Chapel Undercroft. Go there through the Chapel, opening the Average lock by the way. The only problem here is a guard, who shouldn't see you in any case. Sneak past her and get the statue. Back to Waterfront.
It turns out that while you were doing the job, the city guard raided the Waterfront in order to find and arrest Christophe. Methredhel will tell you all the details once you find her. You have to plant the statue you stole in Myvryna Arano's house (leave it in a closet). Find Hieronymus, who's hanging around somewhere, and tell him that Arano was the one stealing the statue. You'll have to persuade him a bit to make him believe. Follow him to her house. After a short scene wait for some time and Armand will appear as usual at midnight in a given place.
You'll get a promotion and access to a new fence - Dar Jee in Leyawiin. Next missions will be assigned to you by S'krivva in Bravil.
Your new Doyen will send you to Leyawiin in order to speak with Adharji. When you're there, talk to some beggars, then go to her house. She wants you to find a thief named Amusei - remember him? He's the one you beat in a race to join the guild. Talk to some beggars again, and you'll know that the Argonian is being held prisoner in the castle. Go there. In exchange for a lockpick, he'll tell you everything about the ring. The Countess has it.
Again, question the beggars. You have to find Hildara Mothril, countess' handmaiden. She's hanging out somewhere in the Leyawiin Castle. Talk to her, rising her disposition, and she'll tell you some useful things about Countess' habits and a secret torture chamber hidden somewhere in the castle.
Wait until midnight. Go down to the basement and use the lever hidden in one of the barrels (screenshot above). First you'll find yourself in the torture chamber, then go to the Countess' living quarters. Sneak past her and either picklock the Jewelry box or steal the key to it from the sleeping Countess. When you have the rind, go back to Adharji.
HINT: Adharji will double her reward for you if you tell her that Amusei tried to sell the ring - before you give it to her, obviously.