http://www.njsp.org/info/pdf/firearms/sts-033.pdfThat is the application for a NJ firearms permit. This is not to be confused with a concealed carry permit, this is just a permit to purchase/own a firearm in your state. (Note, it say submit this in duplicate, so print and fill out two of them....I'll save you a return trip by telling you that up front).
Most of the laws and information can be found here (click the "I agree" and it will open the page):
http://www.packing.org/state/new_jersey/Start there, and there are links to New Jersey specific forums on Packing.org (on the right side) that may prove helpful.
I don't have any first hand experience with NJ, maybe someone else will drop in with more specific info.
As a side note, it appears that NJ is not a "Shall issue" state for CCW and they have only issued 3,000 permits (to 8 million people, and most of them are retired officers), so a CCW permit is probably a waste of money to apply for in your state.
Good luck!