Mine stone blocks with a pickaxe
Look for black-speckled coal ore blocks
Search underground in caves and ravines
Check mountain biomes and cliff faces
Mine coal ore with any pickaxe
Use a Fortune pickaxe to get more coal
Smelt charcoal if you need an alternative to coal
Open large cave entrances near the surface
Dig branch mines at mid to high Y-levels
Explore exposed stone in mountains and hills