Once you're familiar with the cycle of fifths, modulation becomes fairly trivial. You start to apply the appropriate corrections "sharpen this, flatten that" simply as a matter of habit.
In fact, this is precisely how modulation arose historically; it used to be the case that all music was notated diatonically or nearly so (only distinguishing between B and B-flat!), but performers would implicitly "add" sharps and flats to make it sound good depending on the context - a practice known as "musica ficta". You're right though that on a plucked string instrument everything looks the same - and historical intabulations (i.e. tablatures!) meant for plucked string instruments are actually an important source that gives us info about how musica ficta was played in many cases.
