We went to the Ground Transportation Center in the airport and asked their advice. We were advised to go on what they called a "shared taxi" which was like a minibus taxi with other people who weren't part of our party.
It cost us $13 each (but this was a couple of years back, looks like it's $14 now)
Whatever you do, do not get in one of the yellow taxis outside the terminal, they are a complete ripoff! And if in doubt, go to the Ground Transportation Centre, that's what they're there for!
I got the bus from Newark to the Port Authority Bus Station, which is on (I think) 8th Ave. It was great for me as it was only about 2 blocks north to my hotel which was only 1 block east of Times Square.