How can I play monsters and NPCs up to their potential?

In many cases discussions about balance in 3.5 will, inevitably, involve one side or another invoking an anecdote of the time they fought this monster, or a member of that class, and they didn’t suffer the problem being illustrated in the discussion at hand. In many cases it seems like these anecdotes come from a case of the monster or NPC not being played (tactically) or roleplayed (again tactically, since that’s part of 3.5’s roleplaying experience, but also in terms of personality) up to the potential illustrated by its ability scores, powers, and skills.

How can a GM learn to play these monsters and NPCs up to their potential?