Know that NJ does not require contractors to be licensed like plumbers and electricians. They must be registered, and that is filling in a short form with the state. Absolutely no qualifications are required.

1. Ask your friends and family for personal recommendations. Ask on this page too, but know that sometimes, a contractor is either recommending themselves, or using their friends to do it. If you take a FB recommendation, follow through on it. Ask for phone numbers of happy clients. Then call them, then ask to take a look if you can.
2. Ask to see a copy of their insurance. This is especially important if you are doing major work. Generally, they should be insured up to $1m. If they have any kind of honesty, they won't mind showing this to you.
3. Compare several contractors written estimates (3-4 is usual), and you will start to see who has left items out and what their number actually includes. You may find one is way higher and another may be considerably lower. The professionalism in the type of bid can be a good clue. I have had bids handwritten on the back of an envelope consisting of 5 lines.
4. Trust your gut. If something sounds too good to be true, it probably is.
5. I can't tell you how many times I have seen poor workmanship, caught contractors out on a lie and that includes whether they actually applied for permits or not. A bit of legwork on your end at the beginning, can save you a whole world of trouble during and after construction.