When I was a kid on summer vacation I used to drive an ice cream truck that way every day for a while.
That was way before 280 was built also.
Looks like I used to take option 3 of these, but here's a quick start with 3 various choices:
If you mouse down under Driving Directions 3 different options appear, me, I'd go for #1 or #3 or also explore getting on I-280. You can do that by dragging the blue line over to it various ways.
Fairfield, NJ to Jersey City, NJ - Google Maps