Warm up. Your lips must not be brittle or stiff when you practice to extend your range. A slow, relaxed daily warmup will improve your chances for success. Begin your routine with lip slurs, scales or intervals; be sure to use plenty of air and go after the best tone possible from the first note of your practice session. Practice with moderate loudness and in the low register. An excellent daily starter is a routine of slurred scales, up and down, rising by half-steps. After a few minutes, you can "touch" the high register, but don't hang up there yet.
Be fresh. Once you have warmed up your lips (this may take 15 to 20 minutes), you're ready to begin with the "meat" of your practice session. Even if you plan to focus on the high register today, it's crucial not to "kill" your lip by practicing up high for too long. Rising arpeggios that ascend into your top range are a good practice technique, as long as you descend again to the bottom note with your biggest, fullest tone. To stay fresher longer, always balance your "screech" practice with middle-register lyrical playing on melodic etudes like the Bordogni Vocalises (see Resources).
Relax your mind. Sometimes, the barriers to playing higher are mental rather than physical. For instance, if you feel high C is your usual "limit," your efforts to play above C may yield inconsistent or just plain frustrating results. Sometimes, learning a new technique can help you overcome the mental barrier. Many players think only about lip strength, when other factors like air speed can have just as great an effect on high playing. High notes that a classical trumpet player may find intimidating can be fairly routine to jazz players, possibly because jazzers think about the high register in a more casual way.
Realize that air is the key. Many fine high-trumpet players will tell you that the speed of the air you blow through the instrument is the biggest factor in successfully producing very high notes. Down low, you want to use lots of air in a wide stream to fill up the tone; but up high, it is much more effective to "blow faster" in a thinner stream. With practice--using lyrical, melodic material--you can learn to "transition" your airstream as you ascend.
Practice proper lip formation and placement. The "embouchure"--the proper name for how you set your lips to produce a tone--is very important to any brass player. This is the most difficult aspect of brass playing to absorb through reading or self-teaching. Having a qualified teacher look at your embouchure and make comments can be tremendously valuable.
Think about tomorrow. Brass players have to make sure they don't strain so hard in a day's practice session that it will adversely affect tomorrow's playing. Even if you're having a breakthrough and punching nicely into the stratosphere, make sure you don't linger there too long, or you may face stiffness, soreness or poor response in your lips for several days afterward. A good "warm-down" each day helps here--play low, slowly, softly and smoothly, almost in the same way that you begin your daily warmup. A few minutes spent doing this after any strenuous practice session or gig can make you much fresher for tomorrow.