Before the Europeans came to the new world with their iron knives and guns, all the Indians had were the branches above them and the stones beneath them, which were very useful. Combine those two things and you have the powerful bow and arrow, with a razor sharp obsidian tip on the end.
When the atoms in a particular mineral or other substance crystallize, they hook on to each other in a regular formation, enabling stronger bonding. If those atoms are not in crystalline form, but in random, or amorphous sequence, the product is not very strong, and in many cases, brittle. Obsidian is the same thing as glass, except not man-made.
Silica bonds strong, but all physical bonds can be broken, and once obsidian does break, it fractures into a very sharp, conchoidal edge, which can be used and made into spearheads and arrowheads. The process of flaking obsidian (or flint, which fractures very similarly to obsidian) to a sharp point is called knapping.
The knapper (or knapist, I suppose) chooses a piece of obsidian closest to the desired shape, sits down and puts a thick piece of cloth or leather on his/her thigh (you can probably guess why). Then the knapist puts the obsidian on his thigh, and uses a deer antler to flake off small chips of obsidian until the edge is sharp all around. Deer antler is best to use because the trick is to apply pressure to the obsidian until a flake flakes off, so a strong but not hard tool is best. Using, say, another stone to break off the flakes, you don’t have enough precision, and too much power, resulting in a crack down the middle. Anyway, the knapist breaks off flakes all around the piece, and then breaks off the top, using that piece, as shown below: (photo credit: Wikipedia)After that, the knapist finishes in the details, such as the grooves in the side to attach it to the arrowhead, and sells it to a young enthusiast, who either uses it to make his own arrow, or for decoration.