Which actions result in experience?
The system is levelled - you won't find hugely difficult things you cannot beat. Except giants.
Actions that level up skills:
- Attacking someone with a weapon
- Casting a spell on someone or something (things like Clairvoyance do nothing)
- Sneaking and not being seen in the presence of enemies
- Opening a lock - seems breaking a lockpick also gives skill xp
- Picking a pocket
- Buying or selling something.
- Successfully persuading/intimidating someone
- Training
- Some quest rewards (Finding Amren's family sword gives you +1h and +block)
- Creating a piece of armour or a weapon, or improving one
- Enchanting/disenchanting something
- Taking damage whilst wearing armour
- Making a potion or a poison
The list isn't exhaustive, though.
I've compiled here some Arqade questions that ask about the specific skills:
Combat
Archery
What is an effective way to level Archery?
Block
How to quickly train Block in Skyrim?
Heavy Armor
Optimal way to increase heavy armor skill?
One-handed
- How does the game know when to increase the one handed weapon skill?
- Are stacked one-handed damage perks additive or multiplicative?
- Where can I train one handed weapons?
- What is the best way to level up One-Handed in Skyrim?
Smithing
What is an effective way to level smithing?
Magic
General
- Do I level up a spell faster by casting often or by casting longer?
- How do spells affect skill leveling?
Alchemy
What is the fastest way to level up my alchemy skill?
Alteration
How can I quickly reduce the magicka costs of Alteration spells?
Conjuration
What's a quick way to level conjuration?
Destruction
Best way to level destruction?
Enchanting
Efficent Enchantment Skill-up
Restoration
What is the best way of leveling restoration?
Stealth
Light Armor
How can I improve Light Armor as an Archer?
Pickpocket
- How can I improve my pickpocketing?
- What is pickpocket experience based on?
Sneak
- How can I learn sneaking effectively?
- How do I get better at sneaking?
Speech
What is the fastest way to level up my speech skill?