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.
Clicking valves, or clicking the instrument with objects. Possible, but more effective with larger instruments.
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).
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.
The Orchestra: A User's Manual is a free resource and will remain so. It still receives between 8,000 and 16,000 unique visits per month from all over the world. See the testimonials. Thanks to all the donations, I have been able to create this responsive re-design. But the movies and sound clips recorded in 2004 do show their age. I would really like to re-record everything and add many more techniques, especially for solo and ensemble writing. I estimate this will cost around £30,000. If you know a source of such funds, please contact me: a.hugill [at] bathspa.ac.uk