For the most part the advice above is dead-on.
For the 'little' guys (either on the short end or the light-end of the scale) learning to stunt like the big boys means that you have to work more on certain muscle groups and more specific stunting techniques. When you can shoulder press a 100 lbs dumbell with one arm, with ease, then muscling stunts into place is also easy -- if you can't, then you have to be more precise in positioning yourself under her center of mass to make stunts hit.
As mentioned, legs are the key to a great toss. Not necessarily the strongest legs, but the most POWERFUL. They should be explosive. Plyometric style exercises (box jumps, etc.) are as important a component as doing pure strength drills (like the squat or leg press).
One of my personal favorite exercises, though one that is NOT highly recommended due to the higher risk of injury, is barbell jump squats. I will usually load up an olympic bar with 185 lbs, squat down so that my hips come to below my knees then explode upwards into a jump (my feet leave the ground) and come right back into the squat. Some things I ALWAYS keep in mind when doing this exercise: I always do it either in a cage or with a squat rack stand so that I can't go too deep; when I explode into the jump I am pulling down on the bar so that it stays seated on my traps (and shoulders) throughout the movement -- the last thing you want is it coming up a few inches and then smashing down on your neck vertebrae when you hit the bottom of your landing; when landing the jump I use my muscles to decelerate so that I come to a rest at the bottom rather than just letting gravity drag me down there; keep your core tight throughout the movement, from bottom all the way through the extension in the jump; NEVER lean forward, keep your chest up. This exercise can also be done holding dumbells and is a lot safer that way, but I find that when I do that I tended to let myself get sloppy in the execution.
In addition to powerful legs, stunting requires that you are able to maintain your core (abdomen and lower back) in what I will call a 'hardened' position. You should be flexed with a slight pelvic tilt but not to the point where you are straining to hold the position or hold your breath. I believe a term for it is increased intra-abdominal pressure. Think of how you would naturally react if someone was just about to give you a sharp jab to the gut.
Next up, the shoulders and triceps muscles. These are critical to all overhead skills. You can hit stunts without being really strong in these areas but these muscles are the ones that help you save those that are a 'little bit off'. Get them to a reasonable strength by doing shoulder press exercises and dips. Change them up and find the ones that you like best, then change them up again to give the muscles more to grow into. You aren't looking for size here, just increase strength.
Again, I love to go back to the big bars for developing my basic strengths. When I introduce people to this exercise I've labelled it a 'hanging power press'. I'm sure somewhere out there is a proper name for it but this works for now. Load up an olympic bar with a reasonable amount of weight -- for me that's 135 lbs but when I started doing this exercise I was working with 95 lbs (and sometimes less). Now unlike most olympic style lifts (clean, snatch, etc.) that start with a very wide grip, you're looking for a shoulder width grip on this one. Grasp the bar with an overhand grip and then stand up with it, using your legs not your back. From this 'hanging' position, the bar will be resting against your thighs, you lower down until the plates nearly touch the floor, keeping your back aligned and sliding the bar down just along (but not touching) your legs. Explode from that position pulling the bar upward to chin height and 'catch' the bar at shoulder height. Do NOT squat down to get under the bar! While this is the proper technique for an olympic style press that is not the point of this exercise. If you find yourself doing that to get the weight up then use less weight. Rest for a heartbeat or two, just long enough to have full control of the weight and focus on 'hardening' your core and having a proper, upright, posture. Then do a half squat, that would be a squat that goes only half as deep as your regular squat, and explode upwards with your legs. The point here is to use the power of your legs to drive the bar to extension overhead rather than slowly muscle it up. Lock your arms out at extension and stabilize the weight. Once stable, bring the weight back down to shoulder height and then back to the starting position in a smooth and controlled two-step motion. Repeat 5-8 times then rest. Again, because of the explosive nature of this type of exercise you need to do it with strict form and the 'right' weight range. Too heavy and you will be doing the lift olympic style, dropping into squat and staggering your legs on the press, too light and you may find that you put too much 'juice' into the press and have trouble stabilizing the weight overhead or overextending the elbow joint under weight and cause it to 'pinch'. I've done that one and it took several months for the pain to go away.
Muscle groups that are not really critical to stunting in general: chest, upper back. But don't neglect them either as keeping a balanced physique is always a good thing.
Beware of over-training. Training EVERY day gives your body little chance to adapt in a strength/power modality and forces your body to try and be more efficient (think marathon runner vs. sprinter). Eat lots, get plenty of sleep, and even if you don't bulk up your strength will increase significantly over time and that's what you want most.
Now, while all of that is to help you get ready to stunt, nothing beats actual stunting time. Stunt with as many different flyers as are willing to stunt with you. Don't discuss the fine points of EVERY SINGLE TOSS, just do a lot of tossing and when a consistent pattern develops then you can address it. In the beginning there will be a LOT of little things going wrong all the time. Get in the reps and build that base so that you can refine it.
Have someone who knows what they are looking for watch your toss and give you tips. Find what works for you, but if you hear everyone give you the same critique ("use your legs", or "follow through on your toss") then that's going to be prime area of concern. Pay attention, just because you think you are "using your legs" doesn't necessarily translate to you actually doing it. Sometimes taking a video and reviewing it later can give you great insight into what you are doing vs. what you think you are doing.
Also, WATCH what other people actually do. It amazes me how often people say they do one thing and then you watch them do something completely different. Most people parrot back what they were taught, even though over time they have adjusted their technique to be doing what actually WORKS for them.
There are two styles of tosses, one is more applicable to the shorter guys, and the other to the taller guys. You being over 6' tall should probably lean towards the second style so I'll describe it to you. All guys should start off so that they are in the position where they are holding the girls hips (not her waist, and certainly not way up by her rib cage) and crouched to the point that they are looking at either the back of her head or nape of her neck. Now, you LET the girl start the jump, you follow her down into it mostly by letting your arms extend downward but also by bending your legs a bit more into the squat. You don't want to get into a deep squat because that is not your power zone for a jump, stay above the parallel of your thighs to the floor. When she jumps up follow with your arms so that your hands (and her hips) reach about your chin height and your elbows are tucked along your sides not flared out, then EXPLODE upwards with both your arms and legs at the same time following all the way through on your jump and your arms extending all the way up to the flick. The key to all of this is SPEED. Don't try to toss harder but rather both of you should be thinking of jumping faster. That's the power in the equation. This is all about timing, and sometimes it takes a few tosses with a partner to sort it out (or a few dozen -- or several hundred when you first start out).
There is a lot more I could go into about common mistakes (pulling back on a toss, proper hand positioning, timing of the flick, etc.) as well as each of the overhead skills but then I'd have to write a book. :) (OK, so I actually am writing a book on co-ed stunting technique but no one will see it before the fall of this year.)
Final piece of advice (and one I WISH I had when I first started), don't let anyone tell you that you should learn a chair as your first stunt. Nothing will ruin your potential for a great toss quite as quickly as this. It's far better to learn a decent toss hands, and be working on overhead skills like liberties and such and then, if you feel you must, go ahead and learn a chair for 'completeness'.
Please Note: When I mention weights I am talking about the total weight [bar + plates] with the standard olympic bar being 45 lbs.
