There were two main methods of use:
Throwing it at the target.
Holding it in the hand, and using it as a club.
Both methods were used in hunting and warfare, with using it as a club being more common in warfare than hunting (perhaps because people will throw it back at you). In war, when used as a club, it would usually be used with a shield or parrying-shield.
Note that the only hunting the returning boomerang was used for appears to have been hunting birds (in both Australia and ancient Egypt). The returning boomerang doesn't appear to have been used in war.
The non-returning boomerang, designed to fly straight and level, is a convenient hunting weapon, since it will still hit a target that runs away, while a spear (with a parabolic trajectory rather than a straight-and-level trajectory) will miss.
A thrown boomerang of this type can hit very hard. They usually weigh about 400-500g (about 1lb), and they can hit with kinetic energy in excess of 100J, comparable with a blow from a (hand-held) club, or even more effective.
For more on boomerangs as weapons, see my past answers in: