I've had a couple of boomerangs over the years.
Picked up a few while down in Australia that are the typical sized, one is hand crafted/carved while the other is a piece of thin plywood that is machine cut. After I learned how to throw them I picked up some semi-custom hand made ones as well. A buddy of mine has a couple that cost between 50-70 bucks a piece and have custom weighted tips to make them balance and fly properly.
There are right handed and left handed boomerangs. Really, it doesn't matter which hand you throw them with but it DOES matter which bit of the air foil cuts into the wind. If you have a right handed boomerang the flat part of the air foil will be in the palm of your hand. It's just like an air plain wing in that the part of the air foil you want biting into the air is the thick meaty part followed by the thin trailing edge.
You can throw a left handed boomerang with your right hand but you just have to make sure that it's air foil is arranged in your hand properly and it is going to fly it's circle in the opposite direction when it returns to you.
When you throw them....
First thing you need to know is that it takes surprisingly little force to throw some boomerangs. They are an aircraft wing and they are relatively light weight with big wing spans. Of my rangs the amount of force needed to throw them, I'd say it's about like trying to throw a tennis ball 25-40 feet.
Next up, blade angle to the ground. If you throw a boomerang such that the blade is parallel to the ground,
YOU ARE DOING IT WRONG Way to throw a rang is so that the blade is about 5-10 degrees from vertical, 5-10 degrees meaning 80-85 degrees as you hold it out away from you about to throw, not past vertical 95-100 degrees.
Some boomerangs are tolerant of winds and almost need a wind while other boomerangs need almost ZERO wind.
They are absolutely touchy how you throw them into the wind as well. I have found with mine that they are not tolerant of the wind very much, anything over 5 mph and it will blow them all over hell and back. When you throw them, if you have a right handed one which means it will fly out in front of you, cut left, and orbit back around to your left before hovering down for a catch, you need to throw them so they cut into the wind. That means when facing the wind directly, turn clock wise a few degrees at a time until you find the right angle of wind to throw the boomerang into the wind or against the wind. I have to face about 30-45 degrees away from dead on into the wind when I fly my boomerangs if I want them to return to me during a breeze/wind.
How well do they return to me? I've gotten to where after years of not throwing them within 5 to 10 turns I can get them to fly back to within 5-10 paces of where I originally threw. As I warm up that will reduce down to roughly 3-5 paces with the occasional only 1 or 2.
I have caught them one handed in the past but usually I do the typical "clap" where you turn your hands parallel to the ground and you bend your fingers up away from your palms to clap down on the boomerang. Most of the designs out there will climb in elevation as they orbit back to you, as they hover down to the ground above you, you will see a very distinct "ring" from the spinning wings/blade of the boomerang. That ring is what you aim for when you go to grab it.
There are some really funky boomerang designs out there, some have very strange flight paths. We've also thrown as many as three boomerangs all at once by stacking several right handed boomerangs together. Tightest loop on the inside, 2nd tightest loop in the middle, and biggest loop touching the bottom of it's air foil in the palm of my hand. When you throw them they all separate in the air and spread out to fly their own flight pattern.
Then there are the hunting boomerangs. Saw those in Australia and they are COOL but more for decoration. If you were to throw one you are likely going to break it and mess it up after it spins and impacts the ground. I am unsure if they have any that can manage to actually lay over horizontal in flight or if they are all oriented vertically during flight, I'd hope they'd lay over horizontal and fly straight so that they could fly farther like a glider almost. But the big hunting ones are HEAVY. I think part of the reason they might be effective is as they are flying through the air and tumbling, it would be a very disorienting thing for an animal to see because their perspective of it would be that it is growing/shrinking as it arcs towards them. The trailing edge of this thing when it spins around could definitely hit something hard enough to break it's neck or maybe snap a leg.
They have some that are almost as long as a grown man's arm.