The links above take you to the Fish and Game websites of New York and New Jersey. There you can find information about taking the hunter safety course, how much licenses cost, season dates and bag limits, public hunting lands, and much more.
If you plan to hunt with a gun, you should familiarize yourself with your state gun laws. The link above will take you to a page on the NRA website which has good synopses of every state's gun laws.
Online community forums are a good way to meet other hunters and learn about hunting in a particular state.
You can't beat Amazon for its ability to have what you need and get it to you quickly, especially if you have Prime.
There is a huge amount of lightly used hunting gear available on ebay, which makes it an essential stop when looking to get started on a budget.
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The folks at Outdoor Empire have a great breakdown of the rules regarding when kids are allowed to hunt in every state. In NJ kids 10-13 can hunt for free when accompanied by an adult mentor.