Set multiple fire keys. More fire keys will help you shoot more bullets at once. Many players use the "Z", "X", and "C" keys for this purpose. Scroll down is a big help rather than just using left click. However, using the scroll button to fire is a disadvantage, as your bullets are often too close together, allowing your opponent to easily drive around them.
It is also important to keep a count of how many shots you and your opponent have left. If you are out of ammo, you should seek cover until you can reload. If your opponent is out of ammo, you should try to rush him while he is reloading.
For league play the biggest radar is usually the best. Being a good dodger will improve your skills.
Increasing the radar size is not sufficient. The bullets must be highly visible; increase their length and size till you see them very well.
Keyboard or Mouse?
When you're first starting off playing BZFlag, you might notice there are two options; mouse or keyboard. The mouse can be much better, depending on the map, or the keyboard could be better in certain situations. The mouse is preferred in general, simply due to the broader range of control and precision. The majority of players use the mouse, especially in leagues. The keyboard can difficult to use in a close battle, but becomes easy to use with practice, as does the mouse.
Watch other players.
Follow other players in observer mode. See how they move. Try to pick up little things about their playing that will make you better. It may take some time to do this, but trust me, it'll be worth it.
On some maps teamwork is required to get what you need. Always have a good communication system with your teammates, and try not to flood the team channel with apologies for TKing.