Unless your friend lives a distance, it would probably be easier if he picked you up. There is bus service to Penn Station where you can switch to the subway. I would not recommend this if you have a lot of lugguge. There are cabs/limos also but they tend to be expensive. Check out panynj.gov and njtransit.com.

There is a train that runs from Newark airport to Penn Station NYC, from there you can take the subway. Should not be too hard. The train from Newark takes 20 minutes (much quicker than the bus). You will just need to find out which subway line your off in Brooklyn.

I live in Brooklyn and have taken public transit home from Newark many times. First, you have to get into Manhattan. There are two ways: bus or train.

If you choose the bus, you will find a counter down near baggage claim, where you can buy a ticket (I think it's $10). Tell them you want to go to Penn Station in Manhattan (NOT Newark Penn Station, an entirely different place). They will tell you where to wait for the bus - it's right outside. Once you arrive at Penn Station/8th Avenue, there are a couple of different subways ($1.50 per ride) right there that can take you to Brooklyn. (I live near Brooklyn Heights, I take the A/C train). Where in Brooklyn do you need to go??

If you decide to take the train from Newark into Manhattan instead, look for signs in the airport for the "Air Train". There are ticket machines right there in Newark; indicate you want to go to Penn Station NYC (roughly $11.50 for the trip). You get on a monorail which takes you to the Newark Airport Train Station. Then you just wait for the next NJ Transit train going your way. Unfortunately there can be 1/2 hour wait or so. Do NOT get off at Newark Penn Station, the first stop, get off at NY Penn Station. From there, take the subway to Bklyn.

This whole trip is really not tough and takes about the same amount of time as driving, or maybe even less, considering the traffic at TWO river crossings!