guidance systems for icbms are literally the exact same guidance systems used for launching satellites into orbit. that's what the 'b' stands for: 'ballistic' means that the reentry vehicles go where i, the launch vehicle, throw them (βαλλω) rather than guiding themselves to the target with onboard thrusters or airfoils or something. the only difference is that you fall short of orbit
https://en.wikipedia.org/wiki/Ballistic_missile
in the 01950s, guidance systems for orbital launch were a very significant engineering challenge. a rocket is almost an inverted pendulum in the sense that it's a long, stiff thing being pushed up from below; even going to space instead of arcing back into the turf near the launch site requires active negative-feedback control. even the smallest programmable computers were too big and heavy to put into space, so they had to use circuits wired up specifically for the guidance and control task. inertial measurement units were artisanally-produced gimbal-mounted things the size of a small child, there was no gps, and cybernetics was in its infancy. my grandfather built guidance systems for icbms at the time, and it was very difficult indeed
now, every twenty-dollar cellphone contains the necessary ingredients, although some of them are artificially crippled by export restrictions, and control theory is a standard course in any undergraduate engineering curriculum, using the inverted pendulum as a homework exercise. and if you're going to spend a few thousand bucks, and aren't north korea trying to circumvent other countries' export restrictions, you can easily get lower-noise imus than the ones that go into cellphones
so yeah, it's easy, even if it wasn't a problem spacex had already solved