The basic ways of Finding Coal or Charcoalare finding a Underground Cave & Digging to find it.
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There are no fireball potions in Minecraft but to make a fire charge you place a coal, gunpowder and blaze powder anywhere on the crafting grid to get 3 charges.
Coal is very common. Caves are a good source of coal, but if you are mining, coal is most common at y=48.
A single piece of coal can perform 8 furnace operations in minecraft 1.6, so that means 8 pieces of cobblestone.
To get coal in Minecraft you will need a pickaxe. The pickaxe can be made of wooden planks, cobblestone, iron ingots, gold ingots or diamond gems. You craft it by doing 2 sticks up the middle and 3 of whatever material along the top row in a 3x3 grid (right click a crafting table). Coal is obtained by destroying coal ore - it is stone with black markings in it. Destroy with the pickaxe to get the coal. You can then make torches with it or use it as a furnace fuel.