Breath attacks
Blowing through the instrument. There are seven pitches available on most trumpets, and more on the piccolo trumpet. The pitches are fairly indistinct, though. Notate with a verbal instruction, with pitches indicated if required.
Breath attacks:
Clicks
Clicking valves, or clicking the instrument with objects. Possible, but more effective with larger instruments.
Multiphonics
Multiphonics achieved by singing into the instrument are possible, but not as effective on the trumpet as on larger bore instruments. Played multiphonics may also be achieved by splitting partials (playing between the "C" and "G" registers etc. and sounding both). Pretty clean 3rds, 4ths, and 5ths may be achieved this way with practice (thanks to Mark Goldstein for this comment).
Multiphonics:
Microtones
Intervals smaller than a semitone. Notations vary, but the examples
above show a microtonal inflection and a quartertone. Microtones are practicable, but obviously need a great deal of care and attention to detail. Consultation with the player is probably the best way forwards.
Microtones: