Sadly, trills are rarely perfected, but with some meticulous work they can and should be. Trill drill is definitely worth the extra effort. Trills can dazzle your listeners when deftly executed. Your goal is snazzy, spiffy, sparkling clear finger-poppings, performed exactly in time. Even if other details are imperfect, your impressive trills can save the day. There is nothing quite as satisfying as that grandiose, confident and well-executed trill at the conclusion of a great piece of trumpet music!
Sloppy trills however, can drain your energy and bore your listeners. Don't be thinking like a truck driver while your fingers furiously flap away for 8 to 10 beats on a single note. Think "flute, soprano, solo violin, butterfly" or anything that flutters gracefully. Remember: trills are not tremolos, buzzers, or anything Black and Decker. Nice trills have two recognizable pitches, usually a major or minor second apart. And there is a reason that the two notes prior to the resolution are called "grace notes!"
Be sure to monitor your speed. Too often trilling is too fast and too intense. The important note in a trill is the first note. The rest are throw-away and less important (as long as they are decent). The resolution is where you are going. Whether you start above or on the note, make sure it is impressive and clean. Never mind the textbooks, just do it nicely!
To stop the trill or not to stop the trill is the question that is usually answered by convenience rather than conviction. How about Plan A. That is: trill right into the grace notes without stopping. This is a bit harder to do as it involves a lot more coordination, but sounds great. Resolving the trill before the graces is O.K. but still sounds like Plan B.
Once you seem to have mastered trills, prepare them in horribly awkward keys! Since we only need to train 3 fingers, we might as well discipline each of them to work for us in any key.
Note: don't forget that for picc work, the 4th finger needs training too.