-Get an axe (hatchet, NOT a battleaxe)
-Cut down a tree (look in the Woodcutting guide if you need help on learning how to do that)
-Get a tinderbox (can be bought at a generral store for one gold coin)
-Drop the logs
-Use the tinderbox with the logs on the grround
-After a few tries you should light the fiire
 

Calculating the Experience
Believe it or not, the amount of experience that you get when you light a fire depends on your firemaking level. As you make more fires, the amount of experience you get for making a fire will get greater. There is a formula you can use to find out how much experience you would get for making a fire. This formula is: (level * 1.75) + 25. So just substitute in your level where it says "level" and your results will be the amount of experience you will get for lighting a fire with that level. For example let's say your level is 20. Then to figure out the amount of experience you would get, you would replace level with 20, like so: (20 * 1.75) + 25. Now multiply 20 by 1.75. You are left with 35 + 25. That results in 60, so every time you light a fire at level 20 you will get 60 experience.

Tips

If you want to level your firemaking quickly, go to a forest
If you want to level your firemaking quickly, fill your inventory with items before you cut trees, then the logs will fall right on to the ground
Firemaking is the easiest skill to level, so if you are mad about skill total, you should level your firemaking
When using coal and a fire together they create charcoal. You must be a member(p2p) and be a crafting level of 10 to do it. Though it doesn't give you any exp in any skill charcoal is most likely an item needed to do something in the future.