For EWR, take any NJ Transit train from Penn Station in NYC that stops at the Newark Airport station; I think the departure board at Penn Station might show airplanes by those trains. You could also take the PATH train that stops at various places in Manhattan, go to Newark Penn Station and then switch to a NJ Transit train for one more stop to Newark Airport, but that's added hassle. You take the monorail from the Newark Airport train station. On weekends the whole process can be kind of slow as NJ Transit trains don't run as frequently as during the workweek.