A good way to look at acid/base reactions is how stable the predicted products are. Frequently, acids are fairly stable after donating a proton to another species—although there are more expansive definitions of acids. Similarly, bases often are stable after donating a hydroxide ion.

Look for potential resonance structures and inductive effects acting on the conjugate acid/base and other basic rules to predict how stable they will be.

Strong ionic compounds, like the KOH you mentioned, will readily form K+ and OH- ions in solution. In water, for example, those ions can be stabilized by solvation and that’s part of why KOH is a strong base.