Most club racing of the hot lapping or time trialing variety will not allow passing in corners. Autocrossing doesn't involve passing at all. However, should you venture into racing which involves passing, or you get in a situation where passing in a corner is inevitable, here's some things to know.
Passing is typically achieved under three circumstances: you utilize your car's greater horsepower or momentum exiting a corner to pass on a straight, you pass under braking by controlling the preferred driving line entering a corner, or you take advantage of your opponent's mistakes.
First rule - it is the responsibility of the driver initiating the pass to ensure that it is done safely. Where you pass, and how you pass must be done in a manner that your "opponent" is aware of.
Second rule - blocking is illegal. Swerving, whether it's six inches or six feet, to keep another car from getting beside you is blocking. Most organizations will allow you one move to protect your position. Repeated left-right moves is blocking.
Third Rule - if another driver has legitimately placed his car beside yours, leave room for the other car to carry a line through the corner. You don't necessarily have to give him the optimum line, but cutting a car off that results in forcing it off course is poor racing, and if the officials see it as deliberate, you're subject to penalty. Racing is not a roller derby. Eliminating your competition is not one of the objectives.
Passing under braking or on a straight close to a corner requires a little more planning than a simple pass on in the middle of a long straight. The object of passing in the braking zone is to control the inside line to the upcoming corner. By placing your car between the other car and the corner apex, the other car must yield to give you room to continue your driving line through the corner. In this manner you have essentially "controlled" the preferred line into the corner.
The potential downside to making this move is that your car will not be taking the turn on the optimum line. You may control the corner entry, but if you have to slow down too much, or make too early an apex, the car you've just passed may carry more speed or a better exit line, and pass you right back coming out of the corner.
During practice sessions, you will need to not only practice the optimum racing line for fast laps when you're clear of traffic, but you will want to practice some passing lines. Move in from the edge of the track where you'd normally drive, brake a little farther and turn in a little later. Practice taking a line that puts your car in the middle of track coming out of the corner, or a least far enough over from the edge so as not to leave enough room to be passed on the exit. (Hogging the road so there's not enough room to pass, but still avoiding the swerving, is not blocking). By practicing these passing driving lines, you'll be ready to use them, and there's less chance that you'll cause an accident when attempting a pass.