There are several different possible breathing patterns during kettlebell lifting. Since it is a sport that rewards efficiency, breathing must accordingly be as efficient as possible. However, you must also adequately protect the spine with intra-abdominal pressure. The tempo of the breathing varies according to the lift you are doing, for example the clean and jerk has a different breathing pattern than snatches. The best tempo is usually discovered through trial and error, but here are some general concepts to get you started.

Breathing during heavy reps

When you are training in the low rep range, the best method of breathing is paradox breathing. In this method, you actively breath into your stomach at the bottom of the swing, where the pressure on your spine is the greatest. This is not a very efficient method of breathing, because you must inhale against the resistance of your body's compression. However, this method offers the most protection and would be the best choice at all times for people with back trouble. At the RKC seminar, I heard many people comment that this technique made their swings painless for the first time ever, so it is obviously very effective.

Breathing during max reps

When the weight is light and you are going for a cardio workout, efficiency is the name of the game. In this case, it is best to exhale on the downswing and inhale as the bell rises to the top. This method is very efficient because you can use your body's compression and decompression to your advantage. I discovered this a few month's into my kettlebell training during a high rep set. While I was able to crank out the reps, it was a bit hard on my back. Since then, I've found the trick to making this method work. In order to keep your breathing efficient, but also protect your spine, you must exhale under tension, like in Power Breathing. By forcing the air out with some pressure, you can effectively increase your abdominal tension, which will help protect your spine. This method will not provide the level of protection that the paradox method will, but it is fine when the weights are light and you do not need the ultimate in protection.

Training for improved breathing

Firstly, practice Power Breathing as described in Bullet-Proof Abs.
Then, add in paradox breathing crunches. Take the lame old crunch, but make it tougher by actively inhaling as you curl your spine up off the ground. You will feel like you are doing a crunch against the resistance of an air bubble in your stomach. As you get better at this exercise, it does everything but get easier. As a matter of fact, it gets much harder because you diaphragm gets stronger.
Third, check out some of Scott Sonnon's material, such as Maximology and Tape 3 of the Zdorovye series, Dykhaniye.

Don't Cheat on Your Pullups!

One of the things I often see in gyms are people cheating on their pull-ups. While I applaud them for getting off the machines and doing a real exercise (I do), they should be done properly for the best training effect.
The first thing I tend to see is a lot of body swing. On bars, you can make it a bit easier by pulling up on the backswing. As people crank out reps, they swing more and more and rely on momentum to keep them going. If you are striving for perfect pull-ups, try to straighten out your pulling groove so that your body does not sway at all. Keeping a tight body position will help for starters. This means that your abs and butt should be tight, your back flat and your legs straight and locked. If you ever see a swinger try some pull-ups on rings it is fun to watch them get cut down to size. As they swing one way, the rings swing the opposite way, canceling out the momentum advantage. The other type of body movement you see is called kipping, which is forcefully raising your legs and then letting them as you pull up. This jumping movement is used to build up momentum, which decreases the strength requirement of the pull-up. It is necessary in some specific exercises, but not the pull-up.
The next thing you tend to see are people that only go down half way before pulling back up. While this technique might have limited use as an exercise in strengthening the top portion of the pull, for most people it is unintentional, improper form. A pull-up should start at a dead hang. You do not have to pause unless you want to, but your body should lower all the way down. Pull-ups are just plain better when performed full-range. They stretch the upper body nicely and strengthen many of the muscles in the upper body through a wide range of motion.