Monsters come out in the dark, so turn on the lights!
Mostly you will use torches to provide light, but a number of other items are practical light sources too.
One stick and one piece of coal or charcoal makes four torches. They're cheap as well as useful!
Torches provide light when you place them on a wall or the floor. They do not provide light when you are just holding them.
Put a torch into a pumpkin and what do you get? A decorative light source.
This block can be found in the Nether. When mined it breaks into Glowstone Dust, which can be reconstituted to make Glowstone.
Preventing Mob Spawning
Every block has a light level between 0 and 15. 0 is dark, 15 is the same as bright sunlight.
A torch has a brightness of 14, the other light sources described above have a brightness of 15.
Each block you travel away from the light source, the light level drops by 1.
Mobs can spawn when the light level is 7 or lower.
How to Space Your Torches
Some tips on how to keep the light level at 8 or above
In a 1-block-wide tunnel, torches may be placed every 13th block (i.e. 12 empty blocks between) if at floor level, or every 11th block (10 blocks spacing) if at eye level.
For a 2-block-wide tunnel, 10-block spacing at floor level or 8-block spacing at eye level will do the trick.
Covering large areas
Place a row of torches with gaps of 11 blocks between them (a torch every 12th block).
Place a parallel row of torches, staggered, leaving a 6-block gap.
Check levels with a redstone torch
If you have a redstone torch handy, you can use it to check light levels. Redstone torches emit a light level of 8. If you place a redstone torch and the square doesn't get any brighter, you know it was at level 8 or higher.
Check light levels by pressing F3
It seems a little bit like cheating, but you can check your current light level where you are standing. The debug screen that comes up shows various information about lightinf; the light level you are interested in is "rl".