It takes a lot of good planning and on board systems which can figure out where in space the spacecraft is and alter it’s trajectory if necessary (spoiler, it’s always necessary!). We have cameras which will spot the asteroid in the distance and automatically correct it’s path to make sure it doesn’t miss it. If you’re interested in that side of physics, the Rosetta mission and flight path is a great way to learn about planetary fly-by’s trajectory corrections and landing on an asteroid.
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