I am a small town country girl traveling to NYC alone for the first time. I will be arriving at the Newark airport.
How do I get to Manhattan from there?
What is the best mode of transportation?
There is a large variety of options for travel from Newark Airport to Manhattan. I have assumed you're travelling to the Port Authority Bus Terminal (as per the bounty), a short walk from Times Square. I have listed them below in decreasing order of both convenience and price.
The following two solutions are included for completeness; I doubt they'd be suitable for yourself.
If your destination is lower Manhattan, you can take the New Jersey Transit bus to Newark Penn Station and then take the PATH train from there to the World Trade Center. This is especially attractive if you have a relatively small amount of luggage, as the total fare is around $6, but it involves carrying your luggage around.
It is also possible to change to a different PATH train that will take you to Christopher Street or to any of four stations on Sixth Avenue between 9th and 33rd Streets.
You have multiple options:
An economical and convenient way to get to the Port Authority bus terminal in Midtown Manhattan is to take the AirTrain Newark (a monorail) to the airport railway station, and from there catch an NJ Transit commuter train to New York Penn Station, from where it is a single subway stop (line A, C or E) to Port Authority terminal.
This route will take roughly 50 minutes and cost 15.75 dollars in total.
There are also direct buses from the airport to the Port Authority terminal, which cost USD 17. However, be warned that congestions on this road, as in much of urban America, can be disastrous and lead to a very long travel time unless buses have dedicated lanes on the road from Newark to New York.