Depends on what special weapons.
The special abilities like the Flare, Soul of Zinglon are activated by pressing space when they're charged (red box in the top left is filled).
The 'twiddles' as they are so oddly called, are performed like street fighter moves - press a combination of buttons in the right order to do it. I don't have the list on hand but each ship in 1P mode at least has their own list of moves, some better than others. :)
Edit: I found the list - [url=http://members.iinet.net.au/~vannevar/tyrian/suprtwid.html]http://members.iinet.net.au/~vannevar/tyrian/suprtwid.html[/url]
Post edited March 25, 2011 by Xenesis