NJ Transit runs out of Penn Station and goes to newark Airport (some Amtracks stop there as well). The Airport train station hooks directly to the airport monorail to get you to the terminals. It takes about 25 minutes and costs $11.55 one way. I've done it before and it's an easy and quick trip. Cabbing it will be expensive and LONG at that time of day. You may go insane being stuck in a Taxi on skins-cowroids day!
Penn Station is at 33 and 7th ave. Be sure to leave some time to get into Penn and get tickets, find the track, etc. Also, leave some time to get to the gate at Newark. GOOD LUCK!
Here's a link to the NJ transit schedule:
New York Penn Station to Newark Airport