1) Flexibility is really all about the tongue. Changing the position of your tongue will alter the speed of your air, and the horn will respond by changing registers. "OH-EE-OH-EE" and "OH-AH-EE-AH-OH" are examples of the tongue positions with which you'll want to experiment. Try to be very sensitive to the relationship between tongue position and airspeed. In general, as the tongue rises towards the "EE" position, airspeed increases- thus encouraging the trombone to "jump up" in register. The reverse holds true as the tongue descends to the "OH" position.

2) Minimize motion in the embouchure. KEEP A STILL CHIN. A mirror on your stand can help you see whether you're minimizing extraneous motion in the embouchure.

3) AIRFLOW is crucial. Constant and steady airflow.

4) Use a metronome. We need to train ourselves to be flexible within a rhythmic framework.

Speed is the desired end in these exercises. Speed and clarity, that is. You will only be able to achieve great speed by starting slowly and gradually increasing tempo over time. This is why you'll use a metronome.

Each day, you should keep a record of what speed you're doing these exercises. Make a note of the metronome setting*. Then, try to increase the setting by a "click" or two every day. Don't go faster than you can play cleanly, but "push the envelope" and feel like you're right at the edge of control. Over the course of days, weeks, and months your speed will increase dramatically.

Basic Routines by Robert Marstellar is a wonderful resource for flexibility exercises.

I have a rather thorough compilation of my favorites written here.

*I have provided a text box for you to enter a metronome marking. After filling in the values,simply take a "snapshot" of this screen each day.... and when you open it tomorrow, you will see what metronome marking you last used. Mac users, screen snapshots are achieved by: command+shift+3 (these snapshots are saved to your hard drive by default). PC users can press the "Print Screen" button on your keyboard. The computer will ask where you'd like to save the picture and in what application.