Learn to adjust your speed without using the brakes.
Learning to ride close to another rider's rear wheel is a matter of experience. If you are new at racing, you probably won't be able to ride on somebody's wheel. You have to feel comfortable enough to stay close to the wheel of a rider without having to concentrate just on the wheel.
You must be aware of everything that is happening in the ride. If you concentrate only on the wheel in front of you, you might miss an important breakaway or cause a crash.
In a pursuit situation, you should ride on the drops with two fingers gripping each brake lever. Just keep a light touch but avoid constant braking, which can cause a yo-yo effect, slow the speed and create a dangerous situation.
When you are riding on somebody's wheel and you are too close, you must learn how to adjust your distance by letting off on the pedals and moving out to face a little wind to slow you down. You want to adjust your speed just by relying on your bike-handling skills instead of the brakes.
A good general rule is to maintain six to 12 inches between your front wheel and the rear wheel of the rider in front of you. If the rider in front of you slows unexpectedly, you should avoid panic and braking hard, especially if somebody is behind you, because it might cause a domino effect of crashes.
As you get more experienced you can get closer. Learning to ride in close proximity is extremely important to racing.