This is a pretty common problem, because if you don’t already know how to throw and catch a boomerang but your rang is also not capable of returning, it’s hard to figure out what the problem is.
Lets assume you have a good boomerang. Most boomerangs are thrown overhand, with a motion similar to throwing a baseball while rotating your wrist like you are cracking a bullwhip. Typically release it at about eye-level, tilted just slightly to the right (for a right-handed boomerang) of the vertical plane. You want to give it some spin in addition to throwing it forward, and depending on the shape it should make a circular or teardrop-shaped flightpath that rises as it flies away from you, and descends as it returns. Wind direction is critical, as you usually throw about 45 degrees to the right (for righties, again) of the wind direction.
To troubleshoot your throw, if it climbs too high initially and then dives to the ground, you’ve either tipped it over to the side too much (you can’t make most boomerangs return by throwing it like a frisbee or skipping a stone), or (if it’s not diving too bad to the ground), you’re releasing it too high - throw down toward the horizon. If it dives initially and then climbs as it turns back to you, your initial release is too low. If it lands in front of and/or to the right of you (for righties again), you’re throwing too far right of the wind. If it lands way off to your left or behind you, you’re throwing too far to the left. If it just peters out in front of you without trying to return, you may not have given it enough spin.
What I recommend is get a boomerang that you know will return, and then figure out how to get it to return to learn good technique. After that, it’s pretty easy to adjust your throw for a different type boomerang. Also, if you’re left-handed there are leftie boomerangs that are mirror-images of the right-handed type. Right handed boomerangs shoud fly counterclockwise, lefties clockwise.
As an aside, the boomerangs you don’t throw as I’ve described above are more competition oriented, and include long distance boomerangs (distance over 100m and return - world record is over 200m) which are often thrown more “laid-over”. MTA boomerangs (Maximum-Time Aloft) boomerangs are designed to settle into a stable hover and so are launched more upward initially (world record around 17 minutes I believe).
Hope this helps! If you’d like I can recommend some good beginner boomerangs, but start either at your local kite shop which might carry Colorado brand sticks, or google for Ted Bailey Boomerangs in Ann Arbor MI, or The Boomerang Man in Monroe LA. Good luck!