While star shot has its issues,handling space dust, micro meteorites and orbital debris (MMOD) at lower velocities is something we already no how to do.
For larger debris in orbit we pick it up from NORAD and maneuver around it.
For smaller debris we can't see with radar we use Whipple Shielding. The outer plate breaks up the particle and deposits it over a greater surface area so it doesn't penetrate.
Vehicles are designed with redundancy so if critical equipment is damaged there's a spare(s) leg available.
For more advanced debris and radiation protection one group was investigating magnetic shielding. They placed a model spacecraft in plasma flow with a strong magnetic field which forces the charged particles around the model.
An interstellar trip would use parts of all of these ideas to design a mission that would have a good chance at avoiding catastrophic damage from MMOD.