(I'm assuming you're talking about vertical shooters a la 1942).
The gold standard seems to be what cave did in do-don-pachi resurrection: http://www.youtube.com/watch?v=lm9cOiydk3w
Basically all movement is relative and basic firing is automatic. Special firing (i.e. bombs) is done by a touch button off the side of the screen somewhere (do don pachi had different configurations where you could put it vertically on the left or right or on the bottom from the left or right). Relative movement means that if you drag left X pixels on the screen, your ship moves left X pixels. Or maybe X * some constant pixels.
Some games have some success with sprite-based control, but you have to make sure that the actual sprite is pretty far above where the actual touch control is so you can easily see your ship. If you do it do don pachi style you kind of get that effect if you start your relative movement on the ship itself, but you get the benefit of being able to touch as far away from the ship as you're comfortable with.