The easiest from LGA to Newark is one of the shuttles that run between the two of them, get on the bus at LGA, get off at Newark. It costs $32 or so though, links on this page.
http://www.panynj.gov/airports/lga-a...nnections.html
The least expensive is any of the methods already mentioned but depending on time of the day it can take considerably longer.
This thread should probably be moved to the New York forum, you may get people with more experience there.