These notes provide some general advice on ways to improve your kata (forms). However many of the methods and tips described below will help improve all areas of your karate, including kihon and kumite.
There are more specific tips on each individual kata on the 'Common Kata Faults' page and tips regarding kumite and kihon are on the 'Kumite Tips' and 'Kihon Tips' pages. All three of these pages combined will help improve your karate in general.
Kata should not be carried out at a monotonous pace (eg 1-2-3-4-5-6-7-8-9- etc.). At the very least, moves should be grouped together to represent defences and attacks against individual opponents so that the timing of a kata is more like 123---45---678---9- for example. Here the first 3 moves are carried out in quick succession, followed by a pause before performing the 4th and 5th moves in quick succession. Then another pause before reacting quickly to do moves 6, 7 and 8. In this way the kata will look (and feel) much more like karate and less like a pre programmed sequence of exercises or a choreographed dance!
Kata involves many more turns and changes in direction than other karate training methods, and this involves performing techniques whilst stepping and turning. Sometimes this can make the technique easier and more powerful, but often the turning makes it much harder to carry out techniques correctly. In particular, when turning in a kata, it is important to ensure that your foot positioning is correct (to keep good balance) and that you use your hips correctly for each technique. Without good balance or good technique (especially hips) a technique will be much weaker and therefore not effective in a real situation.
Whilst doing each kata, try to imagine that every technique is against a real opponent, whether it is a block or an attack - this is the correct way to do a kata. Once you can imagine that the opponent is real, you must then first defend yourself against their attack and then follow up with a counter attack (or counter attacks). This is the bunkai (or application) of a kata (see BUNKAI below).
It is very difficult to carryout a karate technique properly if you do not understand the reason for doing it. For many techniques (simple kicks and punches for example) the reason for doing them is quite obvious and it is relatively simple to understand and imagine the consequences of these techniques. However many karate techniques are more complex and without understanding what these techniques are for, there is little hope of performing them correctly. Therefore when performing a kata it is important to understand what each move is for and the effect it will have on your opponent (see OPPONENTS above). Bunkai is this application of a technique against an opponent and each move of each kata should have its own bunkai. This means (from brown belt and above) you should be able to describe what each kata move is for and how you would apply it in to a real situation, with a real opponent. Without this application a kata is reduced to little more than a physical training exercise.