If you're taking NJ Transit, the best way IMO is to skip the EWR rail station and the AirTrain altogether. You can either go to Newark Penn and take Bus 62 as mentioned above (which is cheapest), or you can go to Newark Penn, Newark Broad St, Elizabeth or N Elizabeth (depending on where your train stops) and take Uber/Lyft from there. NJTransit tickets to EWR include a hefty (>$8) AirTrain fee, so it only costs a little more to take Uber/Lyft the last leg (and can actually be cheaper if you have more than one passenger). For example, from Princeton Junction it costs $20 to go to EWR, but only $9.75 to Elizabeth or N. Elizabeth or $11.75 to NWK. From N Elizabeth (recognizing many trains don't stop there), it's usually <$20 (sometimes as cheap as $12) and <10 min drive to Terminal A where you'll be dropped right at your airline's checkin area. From the other stations it's usually closer to $20 and 15 minutes.