First of all, strengthen your arms by wrists. For this, start boxing with a heavy bag. Hang a very heavy bag, so there is no big swinging rhythm. Begin punching the bag with full speed after standing about an arm’s length.
Keep punching the bag until you feel exhausted. You may find this activity a bit tough in the beginning, but with time you will adjust to the routine. After practising straight punches, try different combinations.
After finishing with the heavy bag punching, perform rope jumping. This exercise will help you strengthen the muscles used for the quick punching. You can add variations by doing sprinting exercises in the 30-second break during the rope jumping.
Using focus mitts with a training partner is another important step. You can try 4-5 different combinations of punches at a normal speed before doing the same combinations at a quicker pace. This will help you determine your improvement.
You are also required to use hand weights during the practice sessions. If you make even only a little improvement with weights during the shadowboxing routine, you will actually be able to pump up your pace significantly once the weights are removed. It is also very useful for strengthening upper back and shoulders.
Practise boxing with a double-end bag. This method of training will surely help you improve your hand-eye coordination as well as hand-speed.
Using a speed bag is another fine technique. Since a speedy bag gives you no time to react, you will automatically be able to increase your punch speed.
After finishing with the punches, you are supposed to work on your reflexes. Consult your trainer to do different reflex exercises. The main objective is to make yourself capable of moving immediately from a relaxed position to a fighting stance.