Anyone who's been to a track day knows there are a lot of rules, and many of them concern passing, such as no passing whatsoever in Group C, passing only on straights and always on the outside in Group B, passing anywhere and anytime in Group A.
Once you get to where overtaking is OK, there are strategies you can use to make your "blew by him" moves as safe and smooth as possible. After all, there are no trophies on the line at a track day--though you wouldn't always know it by some riders' actions and attitudes.
The leading rider is doing more cornering than the following rider, but the following ride
Obviously, stuffing someone aggressively up the inside is both dangerous and ungentlemanly, so scratch this move off your repertoire right away.
Track days, remember, are filled with different riders of varying skill levels, so there's an ebb and flow to the amount of overtaking you'll encounter in each session. Sometimes you'll pass tons of riders, other times none at all. Some you'll pass quickly; getting past others will take time and thought. But when you do pass, keep the following in mind: Watch the rider you're about to pass closely. Observe how they ride, the lines they use, how dramatically they brake. This will help you devise the best strategy for getting by them with minimum fuss.
Don't follow another rider's exact line. There's usually not a lot of fudge-factor in the ideal line around a corner, but there are ways to set yourself up for a clean pass, especially when it's based on a superior drive. Check out these two photos from luscious Barber Motorsports Park. The large image shows riders following one another. The inset shot shows the rider following using a straighter line at the same corner's exit; he's sacrificing cornering for speed, and even though he'll have to turn the bike later on (which this particular corner-exit allows), he'll have already gone by the slower rider by the time he does, and he'll be well-positioned for the following turn.