When performing kicks, I quite often lose my balance, which results in me being positioned in a stance where I'm more exposed to attacks. This is normally due to me trying to raise my leg for the kick, while turning my body to allow my leg to be raised higher.
Are there any exercises and/or stretches that specifically focus on improving strength in the legs and help to improve overall balance when transitioning to one foot?
One of my favorite exercises in that area is holding a side kick against the wall. You execute a side kick with your foot against the wall, and then you shift your weight forward until your foot no longer slides down. This will only work if you hold your leg at least in a horizontal line.
Once you have some balance you can work on height. If you get your foot to face level without losing balance and while maintaining a proper side kick position you will have greatly improved both power and balance.
Note: in the beginning you may be tempted to hold on to something for support. Don't. It'll spoil the whole exercise.
A fun way to work on balance (and endurance) is to stand in your kick stance, and draw out the alphabet with your kicking leg.
This doesn't really work your actual kicking technique much, but it will work your balance and your endurance and strengthen all the muscels needed for kicking, and therefor your balance and technique will improve.
I have vague memories of simply trying various kicks in slow-motion, trying to keep my balance, until I could do most of them without losing my balance.
Alternatively, try to just lift one foot off the ground from a "feet together" standing position. The foot only needs to be lifted until it's no longer touching the ground. Try to keep your balance. After a while, lower the foot and lift the other.
Hopefully, you'll get a feel for how to keep your balance with only one ground contact point.
When talking to people about this specific problem in class, I usually surprise them with my comment: "stop standing on your heel."
If you are light on your heel but strong on the ball of your foot you have several advantages:
In terms of exercise to strengthen those lower legs and the transition, I would suggest jumping jacks. Admittedly, this is because almost all classes will have you do a lot of these so it's an easy sell. Jump rope also works but I never seem to find time....
Concentrate on keeping your weight on the balls of your feet rather than stomping down with your whole foot on each jump. Keep those feet close to the ground rather than bouncing up high. I found that this greatly improved my footwork, my dynamic balance as well as my stamina.
By controlling my effort and using my stronger muscles, I went from 60 jacks seeming like a lot to the point where I'll warm up the class with jumping jacks until I get bored (and they've all turned green :-).
Some techniques to improve balance include getting into a horse or front bow stance, slowly go through all of your kicks 10x, bringing the leg up to chamber, turning between 90-180 degrees slowly, extending your kick, turning back to the original position, then down to the original stance. Once you can do each kick up to 10x without losing your balance, you'll be set.
Another technique is to practice your kicks outside in a yard with uneven grass, such as small mounds. If you master the above exercise, then go to an area with uneven grass, you'll find that you'll once again be losing your balance, though not as bad as if you didn't master the above exercise.
Another way to make it even harder is to close your eyes while practicing the slow kicks because the eyes are a huge factor in your balance. once you close them, you'll increase the connection between the brain, inner ear and muscles and further improve balance even more.
Adding a light weight of 1-2 lbs to the kicking leg, but none to the standing leg, then practicing slow kicks will further increase your balance as it forces your standing leg and brain to adapt to uneven weight distribution. So once you can do that well with a weight on the kicking leg, you should have much more solid footing and thus, solid kicking without the weights.
Also, remember to keep your foot flat as many arts make the big mistake of going up on the ball of the foot when kicking, especially the karate arts. This is very poor because you're losing all your rooting to the ground, which is where balance, stability and power come from.
I would suggest doing kicks or your kata with a blindfold. This is usually much more difficult for older people as well, so if you are taking up the sport as an adult it can be very challenging and you'll get a few laughs out of it too!
To mirror @Vatine - go in slow motion. Get into a stance, slowly bring your leg up in a chamber (that is, knee bent, foot as close to your thigh/buttock as possible) and slowly extend it, then slowly bring it back, then slowly put it down.
Start with a kick about knee high and progressively increase the height. Do this ten times on each leg. If you're just starting, I'd recommend doing one kick a day, or one kick every other day - so ten reps on each side per day or every other day.
In general, you need to be flexible and strong in the hips throughout a full range of motion. Are you squatting with a barbell outside of class? All the way down? What about lunges? Can you do a Cossack with both heels on the ground? Can you touch your toes? If not, you need to work on your flexibility outside of class:
For specific kicking-balance training, I got a lot of mileage out of drilling throwing multiple kicks without putting my foot down. Doing the same kick is easier; switching kicks and directions is harder. When you mess up and have to put the foot down, switch to the other side.
