Welcome to the forums.
OG is the "Original Gravity" of the beer.. this measures how much sugar is in the beer when you begin fermenting, before the yeast turn it into alcohol and co2.
FG is, as you would guess, "Final Graivity" which measures how much sugar remains after fermentation. You compare these numbers to see how much alcohol is in your beer, among other things.
There are a few different methods for measuring this, but the most common is a hydrometer.
It sounds like you are starting pretty much from scratch. I'd highly recommend you do some reading on the basics of brewing. How to Brew by John Palmer is a great way to start. You can even read it online. Here is the super quick, intro to brewing chapter to get you started. http://www.howtobrew.com/section1/chapter1.html
Good luck and have fun