If you've been playing the trumpet or cornet for a while and find that your upper register isn't as strong as you would like, or your lips get tired easily when playing, you may need to work on your embouchure. Your embouchure controls the pitch and the quality of your sound, and without the correct embouchure, it's almost impossible to go from a fairly good player to a great player. While there is no one perfect embouchure - after all, everyone has a different lip and teeth shape - there are exercises you can do to help develop the best embouchure for you.
Use less pressure
Many trumpet players put far too much pressure on their lips, especially when playing in the higher register. Remember, you never want to grind the mouthpiece into your lips. Instead, you want to be aware at all times of how much pressure you are putting on your lips, and try to keep it light.
A great exercise to help you play with less pressure is to play long, soft notes on your trumpet while consciously pulling the mouthpiece away from your lips. The note may break up, but that's all right; simply put the mouthpiece back on your lips and try again. After a few weeks of practice, playing with light pressure will become second nature, and your embouchure will be greatly improved.
Famous trumpet player and teacher Raphael Mendez made his students buzz their lips to improve their embouchures. Buzzing your lips is a great way of developing endurance and control, with the added bonus being that it can be done anytime and anywhere: no trumpet necessary. Simply purse your lips together and make a buzzing sound; you can buzz songs, arpeggios, scales; anything you like. Just make sure your lips are taut but not too tight. Try to blow continuously without breaking your embouchure. Doing this for 15-30 minutes a day should mean you see a real improvement in your embouchure and, therefore, your playing.
This approach won't work for everyone, but give it a go for a couple of weeks and see if your playing is improved at all. If so, graduate to buzzing through your mouthpiece using the same approach.
Relax your muscles
When you play your trumpet, concentrate on producing the warmest, fullest tone you can, and make sure your face is relaxed and your muscles aren't tense. And breath deeply; by doing so, blood circulation to your lips will be improved.
Find a teacher
If possible, find a teacher who can help you while you work on improving your embouchure. It's easy to get into bad habits when playing the trumpet; a good teacher can help identify and fix any old problems and help you develop new, better habits that will only strengthen your playing.