Almost every activity in Minecraft earns you experience. This comes in the form of glowing orbs that appear when you do something important: kill monsters, breed animals, mine special items, smelt ore, etc. Collect these orbs by walking close to them; they reach you on their own if you go anywhere near them!
Levels Require Different Amounts of Experience
Getting from Level 1 to 2 takes much less experience than going from Level 39 to 40. As you progress higher and higher in level, the amount of experience you need to go higher increases. Don’t stockpile levels beyond whatever point you currently need. In general, Level 30 (for Enchanting Table work) or Level 39 (for Anvil work) is the highest you ever need to go. Pushing for levels beyond this yields diminishing returns. You’re much better off spending your levels to enchant something and then progressing in levels again.
Losing Experience
Death causes your character to lose a huge amount of experience. Some of your experience falls to the ground, and you can retrieve it if you make your way back to your corpse in time, but the rest is gone forever.