* Don't get injured. Injury prevention should be your number one goal when training. That means knowing your limits, warming up, and doing 'pre-hab' exercises (these are exercises that don't directly get you closer to your goals, but reduce the risk of injury by training the antagonistic muscles or improving mobility, etc). The weeks you miss due to injury will affect progress more than any other factor in your training.
* Training must by super-specialised. Training works because the body adapts to the pressures put on it by training. But that adaptation is much more specialised than you might think, especially once you get more advanced in your training. This can lead to some surprises. For example, most climbs are most demanding on the fingers (but see section on technique, below), that means doing pullups will not help you achieve these kinds of climbs. Likewise, be very precise about where you are training on the power-endurance spectrum, being able to run for many kms will not help you run 100m any faster.
This also goes for training the antagonists. For example, doing pressups or bench presses makes climbers more imbalanced, not less. This is because it is usually the shoulders which cause more trouble than the elbows (those exercises are good for balancing the elbows). Rebalancing the shoulders requires exercises that bring the shoulder blades back and down, such as rowing-type exercises. Balancing the elbow is also interesting - climbing tends to overuse the brachioradialis (used for pull ups with the palms out or curls with the palms down) vs the biceps, so doing curls (palms up) can improve muscle balance in the elbow, even though the biceps are usually thought of as a climbing muscle.
Also, yoga is terrible for climbers, balance-wise.
* Technique is important. You always think your technique is good enough, but it can usually be better. This is obvious for technique-based sports like climbing and kick boxing, but it holds true for basically all exercise, even lifting weights - my biggest gains in the bench press and deadlift came from technique coaching, and that was starting from 'good' technique.
* Stretch when warm. Stretching is not a warm up and stretching cold is really bad, I got injured this way a few times. This is important for yoga in particular, you really need to go gentle until you are warmed up.
* To train effectively you need to repeat the same thing and make it progressively more difficult. Doing one session of an exercise doesn't make any difference, you have to do that session once a week (or more) for six weeks (or more) and keep increasing resistance or going for longer. However, if you keep doing the same thing for too long, you'll hit a plateau and won't improve. I found this hardest with the things I have most fun doing - I don't want to change them up because I love doing it, but if you don't make changes, you don't keep improving.
* Protein is the king of nutrients, at least as far as training is concerned. I had this vividly illustrated when I turned vegetarian, my performance dropped and I lost muscle mass. I solved that problem with protein shakes and I think getting plenty of protein is the best thing you can do for you diet when training hard.
There is a meme that too much protein is bad for you in some way, but I don't think that is true, at least as long as you have an otherwise balanced diet (plenty of fibre, vitamins, etc.). Research linking excess protein to kidney damage only indicates that if you already have kidney damage, then excess protein can make it worse. No research (afaik) indicates that excess protein can cause kidney damage in the first place.
I haven't found any other supplements to be anywhere near as worth while. BCAAs seem to have a significant but small effect. Some carbs in drinking water when training also seems to help a little. Creatine made a big difference, but the weight gain (in water retention) meant it was not worth it for climbing (except maybe to escape a plateau), and when you stop taking it the withdrawal is harsh, training-wise.