Coal can be obtained by mining coal ore blocks, which can be found all over minecraft in large quantities. Each coal ore block will drop only 1 lump of coal. A pickaxe is required to harvest coal. It can also be found in chests in strongholds and abandoned mineshafts.
Coal is used to create fire charges and torches, as well as acting as a fuel in furnaces and powered minecarts.
Coal is one of the less efficient fuels, depending on the circumstances. While coal can be found almost anywhere, charcoal and wooden planks are often much easier to farm in larger quantities, which often make them more time efficient.
Lava buckets are pretty much always more efficient than anything else in minecraft, though only late in game, when the player has already acquired large amounts of iron and has no other use for it. Up to that point, either coal, charcoal or wooden planks are your best choice. Even though blaze rods burn longer than coal (120 sec. vs 80 sec.), blaze rods are often take much longer to acquire in large quantities, even if you use a blaze farm.
The efficiency of charcoal and wooden planks have been explained in further detail in the charcoal article. The full article on fuel efficiency can be found here.