The Elder Scrolls IV: Oblivion/Stealth Skills

All skills start off at level 5. Once you've made your choice for Major Skills, these will be referred to as Minor Skills. Major Skills start off at level 25. Further skill bonuses can be received through your Birth-sign and Race selection, which will be added on top of the Major and Minor Skills. There are many books & scrolls throughout Cyrodill you can read which will increase a skill by one level. Simply open the book and you will receive a skill increase.

Acrobatics
Governing Attribute: Agility The simple act of jumping, combined with other actions. Anybody can jump, naturally, but skilled Acrobats can jump higher, take less damage when falling from high places, attack in mid-air, and even dodge enemies' attacks with ease.

Leveling Acrobatics Jump all the time, the longer you are in the air the more experience. Falling from high distances works too, just don't kill yourself.

Light Armor
Governing Attribute: Agility Characters skilled in Light armor can make better use of Fur, Leather, Chainmail, Mithril, Elven, and Glass Armors. the higher level you are the more protection it offers, the less it weighs, and the slower it decays

Leveling Light Armor To level Light Armor just let a weak enemy hit you and don't block. This will cause your health to fall much faster so it is best if you have a lot of potions or are skilled in restoration.

Marksman
Governing Attribute: Agility The use of a bow and arrows to attack from a distance. Skilled Marksmen can do more damage, and truly gifted Marksmen also have the ability to zoom in while using a bow.

Leveling Marksman Using targets that you can find around the world you can train your Marksman skill as well as your ability to hit a target you can even get your arrows back.

Mercantile
Governing Attribute: Personality The mercantile skill is primarily used for getting better deals when buying and selling items.

Leveling Mercantile This is a pretty self explanatory one, what ever you find that you don't want to keep and don't need, well go ahead and sell it. If you really want to level this up fast, you can raid some ruins or level practice Alchemy and sell the results, (lots of potions). Bartering will help you gain experience quicker so long as you can sell the items at the percentage you have chosen.

Security
Governing Attribute: Agility When one is trained in Security, they understand all kinds of mechanical locks and traps. The higher your Security skill, the slower the pins will move in the lockpicking interface (or the better chance you will have of opening a lock using Auto Attempt).

Leveling Security You can power level security by buying a large amount of lockpicks, find a very hard lock, and then auto attempting until you get it.

*Note: This skill is made completely obsolete by the reward from the Nocturnal Daedric Shrine Quest.

Sneak
Governing Attribute: Agility The talent of disappearing into the shadows without aid of magic, to pass behind foes without making a noise, and to deal insane amounts of damage by attacking an opponent unaware of your presence. As your Sneak skill increases, the volume of your footsteps is dramatically lowered, your critical damage multiplier is increased, and sneak attacks will eventually completely ignore whatever armor your opponent is wearing.

Leveling Sneak For people at lower levels a great way to train is to go walk behind a guard standing in front of one of the city gates(doesn't matter which city or Guard) Now, auto-walk (tape down the left analog stick or forward movement key) into the wall behind them, ensuring that you are not going to eventually come off the wall.

Speechcraft
Governing Attribute: Personality The use of words to convince others to aid you. As your skill increases, people will have a better initial reaction to you, and be more likely to respond positively when persuaded. The higher your Speechcraft skill, the less bribes cost as well.

Leveling Speechcraft This is a slow skill, play the persuasion mini-game a lot. It will help you out in most quests anyways when disposition comes into play.