Brooklyn to Newark Airport and back
 

I will have access to the F train in Brooklyn and need to get to Newark, preferably via public transit. I will have luggage but will be trying to pack lightly. What is my best route? I assume going home my luggage will be heavier, so I might splurge on a taxi.

Your cheapest option would be to take the F train into Manhattan to Penn Station (34th Street). From Penn Station you can either take a Port Authority bus (I don't know the current price, last time I took it was $7, but I'm sure the price is higher now) directly to the Newark Airport.

Alternately, from Penn Station, you can take the NJ Transit Train to Newark Penn Station, then transfer to the Air Train, which will take you directly to your terminal.

Regarding a taxi, it can be quite expensive to get from Brooklyn to Newark due to the tolls. I think my parents took it once and they paid about $70.

I think a better way to get there would be to take the F train to Grand Central and walk across the street to the Airline Terminal and catch the bus to Newark. The cost is about the same.

I don't think the F train goes to Grand Central, but you can switch from the F train to AC at Jay street to get to Penn Station.