I park at EWR often.
http://www.panynj.gov/airports/ewr-parking.html
P6 is economy long-term parking. It is serviced by shuttle buses that run about every 20 minutes or so. Drivers do not assist you with luggage. The lot is completely outdoors and is undergoing an expansion (lots of construction on the internal roadway). If this lot is full, there will be an attendant standing outside the entrance handing out vouchers. The voucher will allow you to pay the P6 rate at lots P1/P3, which are more expensive. You must turn in the voucher when departing to get the cheaper rate.
Terminals A, B and C all have parking directly across from them. Terminal C's parking is a garage. These lots are the most expensive; I only use them when I have to pick my husband up from the airport.
Lots P1/P3 are also outdoors, but they are serviced the EWR's internal AirTrain system. Stops are P1, P2 (rental cars), P3, Terminal A, Terminal B, Terminal C, P4 parking and Amtrak/NJ Train station at EWR - all in this order and then reversed on the way back. No buses run from here.
P4 is a parking garage situated between Terminal C and the Amtrak/NJ Transit train station. There is a walking path between Terminal C and P4; I have only walked it once and would not do it alone. Sometimes the platform and monorail are pretty crowded. In addition, at times only one side of the monorail is running so everything gets backed up. No buses run to this garage.
We have used offsite parking, which is now under The Parking Spot. We've used the Haynes Avenue lot. The drivers/valets will assist you with luggage getting on and off their shuttle buses. They have promotional coupons online.