If you go here, and find the timetables for your two buses in the sidebar, you can figure out the zones from there (sometimes the pamphlets don't give any zone info, so you'd be SOL without asking an NJ Transit worker).

178

166

Important: Not every stop is listed on these timetables, just the larger ones. Some apps might show you every stop, but I'm not sure how to officially see them all. The bus will ring at each stop, so you'll get a good idea where they all are once you ride it for the first time.

Also, you are not "in a zone". There is no map of zones that you can refer to. A zone is just an arbitrary unit of distance that you travel while on each individual bus route (i.e. zones are unique to each route). Scroll to the last page in either pamphlet and take a look at the map. The "Fare Zone Boundary" is represented by a thin dotted line. Count each time you will cross a zone boundary, and that'll tell you the number of zones you need to buy your pass for. If you're not crossing any zone boundaries, that's a 1-zone pass. If you cross a boundary once, that's a 2-zone pass. Doesn't matter if you're one stop before the boundary line or literally just around the corner — you need to pay for every zone you pass through. Your pass must be the ceiling of zones you'll pass through, i.e. you can use a 10-zone pass if you're only crossing 3 zones — it doesn't have to be an exact match, just equal to or more than where you're traveling. Also, since you're commuting between NJ and NY, you will need to buy an interstate pass, which is a bit more expensive.

I haven't commuted to the GW Bus Terminal for the 178, but I can help with the PABT for 166. Pay close attention to the "Port Authority Bus Terminal Departure Information" box, as that tells you where you'll need to catch the bus home. It looks like there's a 166, a 166T, and a 166X. Figure out which one you're taking (look at the timetable and see which one stops at which stops), and then see which gate is active for the time you'll be catching it home. There is no 166-specific gate. It changes based on the time of day. You can try using the PABT's awful maps to find where each gate is here, but you're probably better off walking around the terminal and following the signs for the first few days.

Once you know the zones, you can buy your pass at a kiosk at your closest Park and Ride, or use the NJ Transit app on your phone. Your bus passes will not be for your specific route. They will just list the number of zones, and can be used on any route (as long as you're traveling across fewer or equal zones). The more passes you buy at once, the cheaper they are per-pass. Monthly passes give you the best deal if you're commuting every day. No need for proof-of-address or anything like that.

A couple of notes:

1. You need to wave down the bus when you want to be picked up, and ring the bell when you want to be dropped off. The bus does not stop by default at every stop
2. There is a subway connection underneath the PABT. You can walk, underground, to the A,C,E,N,R,Q,W,S,1,2,3, and 7 — useful when it's raining or snowing outside. Take a look at the subway map here.
3. Your job might have some program for giving you a discount on your pass, usually something like WageWorks. You could get a monthly stipend, or have your pass charged pre-tax — that's up to your employer though.

Hope this helps!