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Google Maps offers directions by public transit in many areas. Fortunately, New Jersey is one of those areas.
Check out this link:
http://maps.google.com/maps?f=d&sour...8&z=12&start=0
The exact options available will vary depending on the time of day you're looking at (the above link is for a Monday at 9am, which you can change), and some options do have you go into NYC and then back into NJ. But there are plenty of ways to do it via NJT or PATH. (The cheapest options will probably be NJT buses combined with PATH--NJT trains are a bit more.)
If Google Transit won't show you anything with just NJT buses and PATH, post back here and we can figure something out here for you. It'll be a bit more complicated (it'll involve a few extra transfers--I'm thinking NJT bus 62 EWR-Newark Penn, PATH to Exchange Place, and then PATH to Hoboken Terminal, followed by a bus to wherever you're headed in Hoboken), but it might save you $5ish or so over the NJT train options.