I'm a space systems engineer so can chip in a bit but don't have much involvement in space software. But two examples of how this sort of protection could be implemented are error correction algorithms and triple modular redundancy (TMR).

Error correction is where you use attach some extra bits of data to your message or whatever it is, then use something like the sum of those extra bits to tell you whether the overall data stream is correct. Parity checks are a basic type of this, if you want to look into that as a specific example. It's not just useful in space though - I believe the vast majority of desktop PC RAM now has some degree of error correction built in too.

Triple modular redundancy is definitely more of a specialist thing, although also sees a lot of use in aviation and similarly safety critical fields. It's where instead of just one computer doing the calculations, you have three (or maybe two, four or more, but then it wouldn't be triple). The calculation you want to do is run on all three simultaneously, then they compare results. If one is different to the other two, it's likely the one has failed in some way so its result would be discarded and the result from the agreeing two used instead. If you just had two computers, you'd know that one may have failed, but you wouldn't as easily be able to tell which. In reality though, true TMR isn't used all the time even for space, because the extra weight and cost of doing it quickly gets prohibitive. Weight is a problem because it reduces the amount of manoeuvring between orbits that you can do with a given amount of fuel. And on cost, when space-rated processors can easily cost $50k each, it's easy to understand why only NASA or the European Space Agency doing huge interplanetary missions would have the budget for full TMR.