Missiles like a LAWS or Stinger use solid rocket motors.
Despite liquid fuel being preferred for space launchers, for a MANPADS type missile the combination of storability, inertness in transport, low toxicity, and near-zero setup time, along with the very limited performance requirement (compared to longer range missiles) make solid propellant virtually universal.
Don't forget, these missiles are closer, size, weight and performance wise, to a High Power model rocket than to even an SRBM -- and much larger missiles (like the long-running Sidewinder) use solid propellant for the same reasons. Unlike models, however, these missiles are steerable -- various ones either have seeker heads (like the Sidewinder, too large for shoulder launching, but still solid propellant and small by missile standards), or are wire or radio guided. Steering is accomplished either aerodynamically, with movable fins (like the Sidewinder), or by thrust vectoring with either a gimballed nozzle or jet vanes (the last is technology that goes back to the 1940s on the A-4 and Wasserfall).
While solid propellant rockets aren't practical to throttle, missiles typically don't care beyond a timed thrust profile to facilitate operator safety -- typically "big push to exit launcher, short idle to provide standoff from the operator, then cruise thrust". They're then expected to remain under near constant thrust until warhead detonation (or self destruction on a miss).
Some, of course, like an RPG, or WWII bazooka, aren't steered at all; rather, they're aimed like a gun.
Liquid fuels that can be stored and launched on short notice are very toxic (hydrazine derivatives and nitrogen oxides, either of which will kill you quickly). Those that are less toxic require much more infrastructure, as they almost universally use liquid oxygen (which has to be kept a lot colder than dry ice), and that has to be filled immediately before launch -- and has its own hazards.