I don't know about NJ in particular, but in most states, you simply contact the State Procurement department and they can walk you through it. There is, this day and age almost always a website. You simply supply the information they ask for. They will ask for your Co. Name, address and contact information, tax ID, state license if required, products and services your offer, (they use codes so you will have to decide which codes apply) and any certificates you hold, such as minority status and the like. It should not waste more than a couple of hours of your time. After that, you will receive emails from time to time when they are soliciting bids for the services or products you offer. Some don't send emails. You have to check their website for bids. The instructions should be posted and relatively easy to follow. All-in-all it is a fun time. Enjoy!
Doesn't sound like you need much just to bid. Though to do business once you win you'll need a NJ Business Registration Certificate.
Enroll in the eRFP service at www.nj.gov/treasury/purchase and good luck!