Manhattan to EWR on public transit
When I landed at EWR on Thursday night after 9pm, I took the quickest way in, which for me was the Olympia Airport Express bus to Grand Central at $11 (they also go to Penn Station, Port Authority Bus terminal, and have service to some midtown hotels and World Trade Center during limited hours).
Heading home this morning (Monday) I tried out the train/bus option from Penn Station. I boarded a 0907 New Jersey Transit train ($2.50, purchase at ticket machine), and within a few minutes was at the Newark Penn Station, where I connected to a nonstop airport express bus (route 302, $4, purchase at ticket machine too). I was at the airport just before 1000. Total cost: $6.50.