Acrobatics
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.
Governing Attribute: Agility
Power Leveling Acrobatics
Jump all the time, the longer you are in the air the more experience.
Alchemy
The art of making ordinary plants and meats into potions capable of bestowing magic effects. you need at least a mortar and pestle (there is one sitting on a crate during the tutorial sequence in the beginning of the game). Equip the mortar and pestle in your inventory to open the Alchemy window. To create potions, you need to find two different ingredients with one or more effect in common. You can add up to four ingredients (for up to 3 different effects for a single potion, for Apprentice level and up). As your skill increases, ingredients have more potential effects that you may harness.
Governing Attribute: Intelligence
Power Leveling Alchemy
Power leveling Alchemy is very simple and is also a good way to increase your mercantile skill. To power level alchemy simply go to farms, at farms there are usually large amounts of ingredients with similar characteristics (restore fatigue). Collect large amounts of these ingredients until you can not carry any more, then make your potions and sell them at a store. Good places to go for ingredients are the grapevines outside of Skingrad and Odili Farm (west of Weynon Priory), However there are many more places to go.
Alteration
One of the branches of magic that can be used. Alteration is the ability to modify the very physics of the universe. With Alteration spells, you can create magical shields on yourself and others, burden others, or lighten your own load so you can carry more items without becoming over-encumbered. You can also unlock doors from a distance with the proper spells.
Governing Attribute: Willpower
Power Leveling Alteration
Alteration has some nice little buffs you can use on yourself over an over. There is a shield spell you get for choosing it as a main skill that is very easy to train with (takes 9 magicka and is almost instant cool-down). Remember, the power of the spell does not effect the amount of experience you gain.
Armorer
An Armorer can repair weapons and armor to maximize their effectiveness. You need a Repair Hammer to use this skill. Journeyman Armorers can repair enchanted weapons and armor, and more experienced Armorers can also repair Daedric weapons. A master of the armorer skill never breaks hammers.
Governing Attribute: Endurance
Power Leveling Armorer
Whenever you visit a smith or weapons salesman just buy repair hammers and do it yourself instead of paying them to repair your armor. If you want to level even faster, join the Mage's Guild and make a disintegrate Armor spell on self. after you break all of your armor just repair it again.
Athletics
Athletics affects how fast you can run on land, how fast you can swim in water, how long you can hold your breath, and how fast your Fatigue regenerates.
Governing Attribute: Speed
Power Leveling Athletics
Auto-walk into a wall and then go see a movie. Swimming gets skill increases faster then running so if you really want it to go up go jump in a lake. This skill tends to skill up itself without you really working on it if you're like me and run all the time. (This is a good skill to use trainers on)
Blade
Blade governs how much damage you do with daggers and swords. It also allows different melee moves and power attacks.
Governing Attribute: Strength
Power Leveling Blade
Fight with daggers. The more slashes you hit with the better it doesn't matter at all how much damage you do. You could also find a really weak dagger and beat up a creature you summon. (This is a good skill to use trainers on)
Block
Block determines how much damage is reduced when you block and incoming attack. The more you gain in this skill the more likely you'll be to block since it reduces damage more.
Governing Attribute: Endurance
Power Leveling Block
Turn the game's difficulty down all the way (if it isn't already there), then you have two options, you can find a weak monster, tape down the block button, and forget about it for an hour; or you can find a strong monster. if you choose to find a strong monster keep an eye on your health. this trick is made even easier if you are good at restoration and can constantly restore your health.
Warning your shield will slowly disintegrate, once it reaches 0 you will stop gaining experience for block and start training armor. To prevent this carry multiple shields or kill off whatever you are fighting once in a while so you can fix your shield.
Blunt
Blunt governs how much damage you deal with axes, maces and hammers. It also adds new power attacks and melee moves.
Governing Attribute: Strength
Power Leveling Blunt
Use the weakest blunt weapon you can find and beat the stuff out of stuff, it doesn't matter how much damage you do. (This is a good skill to use trainers on)
Conjuration
A Conjurer has the ability to summon monsters and Daedra from thin air to do their bidding, in addition to creating bound armor and weapons to use in battle.
Governing Attribute: Intelligence
Power Leveling Conjuration
The main way is to get a skeleton spell and spam it. Additionally, you can fight or Soul-trap the skeleton while you do this. Remember, the amount of magicka it takes to summon has no effect on the experience.
Destruction
Magical self-defense, in the form of fireballs, electric blasts, or balls of ice. Most Mages would do well in building this skill, while others could use it as a secondary means of defense when one's Fatigue is too low to fight.
Governing Attribute: Willpower
Power Leveling Destruction
The best way would be to lean more on shooting fireballs then slashing swords. You could also spam Flare (that crappy little fire spell from level one) on a monster you summon. (This is a good skill to use trainers on)
Hand To Hand
The ability to fight and kill foes with nothing but one's own hands. While not as powerful as using a weapon (and certainly not as good to block with), hand to hand combat is fast and doesn't use as much fatigue. Higher skill levels give you more power attacks which can be used to paralyze and disarm opponents.
Governing Attribute: Strength
Power Leveling Hand to Hand
Summon a monster and punch it in the face until it dies, then summon another and beat it up. (this is a good skill to use trainers on)
Heavy Armor
Characters skilled in heavy armor will make better use of iron, steel, dwarven, Orcish, Ebony, and Daedric Armors. the Higher your level, the more protection it offers and the slower it decays.
'Governing Attribute: Endurance'
Power Leveling Heavy Armor
Power leveling Heavy Armor is the same as block, except don't block (duh). 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.
Illusion
Skilled Illusionists can modify the way humans perceive reality - casting light, becoming invisible, or charming others into believing that you are a friend.
Governing Attribute: Personality
Power Leveling Illusion
The best way to power level illusion is to rapidly cast weak light spells.
Light Armor
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
Governing Attribute: Agility
Power Leveling Light Armor
See Heavy Armor
Marksman
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.
Governing Attribute: Agility
Power 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. (This is a good skill to use trainers on).
Mercantile
The mercantile skill is primarily used for getting better deals when buying and selling items.
Governing Attribute: Personality
Power Leveling Mercantile
The easiest way is to use Alchemy and sell lots of potions( See Power Leveling Alchemy)
Mysticism
This branch of magic can be used to detect living creatures through walls, trap souls within soul gems, and levitate items across the room with telekinesis.
Governing Attribute: Intelligence
Power Leveling Mysticism
The best way to power level Mysticism is to use a weak detect life spell over and over.
Restoration
Cast spells to restore, fortify, or absorb physical and magical attributes, cure disease, and resist magical attacks. This is one of the most useful magic skills in the game and should not be left off of any list
Governing Attribute: Willpower
Power Leveling Restoration
Use a weak restore health spell over and over and over...
Security
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).
Governing Attribute: Agility
Power 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 Nocturnal's Daedric Shrine Quest
Sneak
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 taking an opponent unawares. 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.
Governing Attribute: Agility
Power leveling Sneak
For people at lower levels a great way to train is to break into someone's house shortly after they go to bed then auto-walk (tape down the Analog or key) into the wall while they sleep. Once you reach a higher level you can sneak quickly behind people with out them noticing, go to the imperial palace and auto-walk in the corner next to the palace guards. if you have a high enough sneak then they will not see you. this is better than breaking into someone's house because it is not a crime if you get caught.
Warning If you leave your character in auto-walk inside someone's house there is a chance that you will get caught. keep a close eye on what time it is.
Speechcraft
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.
Governing Attribute: Personality
Power Leveling Speechcraft
This works when using an analog (i don't know if it works on a computer). find an insignificant person and play the persuasion minigame. Rapidly tap X and Rapidly spin the analog in a circle, you can complete a game in about a second, increasing your level very fast.