I cannot figure out how to fire a rocket. I can get a rocket-launcher-man to go stand somewhere and aim, but I can't figure out how to command him to acutally fire the rocket, much to my annoyance. What do I need to click to get him to fire (say, at a random piece of wall he's aiming at)?
Either select the unit standing still or one of its waypoints, you should click-drag the 'aim' marker (to the top-left) to the location you wish to fire at, like so:
The unit will then pause at that point of its orders and fire a rocket in the desired direction.
It is important to note that they will stand still for 0.65 seconds1 before firing and that there is a 4.35 second1 cooldown between shots (meaning effectively one shot per turn), and they will stand still waiting for this hidden reload timer to expire before firing. Both of these delays can lead to the illusion that the unit is not firing, even when you've issued the correct orders.
1. See the wiki page for Unit Types
If you command your rocket man to Aim (not the Look command), he should fire his rocket in the direction he's aiming automatically. There's nothing else to it, as he won't fire on sighting an enemy like the other units.
There's also a pretty substantial reload time for rocket units, so be careful of that.