Grossly simplified reply follows - see the classification forms on the main web site at
http://www.pcasdr.org/forms/AXRegForm.pdf for more information. Full details are in the Zone 8 region competition rules, but the registration sheet should suffice for now.
There isn't really an "N" class.
Everyone starts their car in xSS (where "x" is the overall car class, "N" in your case) - "SS" stands for "Street Stock" (or "Showroom Stock"). If your car hasn't been modified at all since it was delivered through a dealer, you start there, with 0 points.
If you modify the car (add 3 or more points for modifications, including special tires), you then move up to "xS" ("Street").
If you further modify (total of 7 or more points), you move to "xP" ("Prepared") class. When you hit 21 or more points, you go to "xI" ("Improved"), and at 41 or more points, you become a "Modified" vehicle (and usually switch classes to either "KM" or "AM"). At 54+ points, you are considered a full "R" ("Race") vehicle and go into the "AR" class.
In your case, a stock 930 would start as NSS. Adding 285 tires adds 2 points, which still allows you to run in NSS. If the tires are street tires of "R" or "C" compound and/or have a tread wear rating of 200 or less, then you would bump into the "NS" class (since you would then have 3-6 points, depending on the wear rating). If you ran race tires (e.g. Hoosier slicks), you immediately get kicked into the I or M classes (and add 6 points for tires).
If you weren't the original purchaser of the car, are you sure there were no aftermarket modifications by previous owners (suspension upgrades, etc.)? If there were, you may have additional points assessed and wind up in NS or NP. The guys at Tech Inspection at the February 12th AX can probably help identify any additional modifications.