Fallout 3 Skills

There are 13 skills in Fallout 3, each associated with a SPECIAL statistic. Skills can be ranked up by using points earned every time the player levels up.
Skills and Linked SPECIAL Stats
1. Barter - Charisma
2. Big Guns - Endurance
3. Energy Weapons - Perception
4. Explosives - Perception
5. Lockpick - Perception
6. Medicine - Intelligence
7. Melee Weapons - Strength
8. Repair - Intelligence
9. Science - Intelligence
10. Small Guns - Agility
11. Sneak - Agility
12. Speech - Charisma
13. Unarmed - Endurance
Skills, the New Version

There are 13 skill available in Fallout 3. Previous Fallout games had 18 skills and some of these, Gambling and Outdoorsman for example, were removed from the game entirely.Planet Fallout: Fallout 3 Skills Traps and Throwing were combined into the single skill Explosives, Doctor and First Aid were incorporated into Medicine, while Steal is now called Sneak.IGN: Fallout 3 Game Guide - Fundamentals
About Skills

The player does not start the game with all skills; they must be learned. Each time the player levels up, he earns points to distribute in any of the 13 skills. Note that the maximum level the player can attain is 20, so the number of skill points is limited. This means the player cannot specialize in everything at once.
Each skill is associated with one of the seven SPECIAL statistics, so it's important to keep in mind what type of character you want to play when starting a new game.IGN: Fallout 3 Game Guide - Fundamentals