I get asked all the time, so here is my story, and I am sticking to it!
Trumpet is a frustrating beast sometimes... but here are my basic suggestions...
1. Take relaxed, full breaths. Keep air support steady, and lift and push with your diaphragm muscles when you you want to play higher and/or louder. Don't close off your throat ever!
2. Play softly and keep the lips together to get a clear tone, especially at first. Pucker your lips slightly forward... don't smile/stretch your lips. Putting your lips to the horn in a relaxed natural manner is the best route and is the most sustainable when you start to play harder.
3. Play long tones... DAILY... aim for 30 seconds without wavering. Start in the middle of your natural range and move up the notes in 1/2 steps
4. Rest as often as you play , ie: ON for 1 minute, OFF for one minute, working up to ON for 5 minutes, OFF for 5, 10, etc
5. It is better to play 10 minutes every day than 30 minutes every 3 days, but 30 mins every day is a good goal for a newbie. Two hours a day for pros...
6. Listen carefully to what you are playing and what pitch and rhythm is happening around you, whether playing with a group or with records.. playing with ANY records/CD is good.
7. Make every note count: Try to 'hear it' in your head before it ever comes out, and when it does, 'place it' accurately and confidently
8. Learn to READ music and learn to LISTEN to music, you need both skills to improvise and make the trumpet fun!
9. Use a metronome if possible and learn your chromatic scale as high and low as you can go, fluid and smooth... start slow and make it even. Add major, minor, etc scales as you go.
10. K.I.S.S. (Keep It Simple Stupid) Playing a few confident well chosen or pretty notes is way more satisfying than spewing a hot mess.... ;)