Read John Palmer's How to Brew (first edition, although a little dated, is free online:
www.howtobrew.com)
Read Charles Papazian's Complete Joy of Homebrewing
Be patient. Don't be afraid to ask questions. You've found a good community here. What kind of a kit did you order? There is an entire section of the site dedicated to recipes, check out the banner at the top of the page and you'll see it. You can also check out sites like Brewtoad for more recipes. I'd recommend starting with some kits of styles you know you like, then branch out from there - this gives you a chance to get your process down while you brew beers you like. It will also give you a chance to learn how different ingredients work together which will help you in formulating your own recipes later on.
Specific Gravity is just a measure of how dense your wort is compared to water. Water will have a SG of 1.000. When you dissolve sugars in it (malt, honey, corn sugar, etc...) the density increases. When the yeast eat the sugars to create CO2 and alcohol, the density begins to get lower again. Eventually, the yeast run out of sugar that they can eat, so the gravity reaches a terminal point - this is the final gravity. You'll know you hit it when it remains the same over 3 or more days.
Generally, brewing goes something like this:
Make wort
Cool wort
Take specific gravity (O.G., or original gravity, before fermentation)
Pitch yeast
Wait 2-3 weeks
Take specific gravity
Wait 3 more days
Take specific gravity again - as long as it is the same as the last reading, you have hit your F.G., or final gravity
Bottle your beer
Store bottles at 70*F or more for 3 weeks
Make more beer
After 3 weeks, cool some bottles in fridge for a week or so
Enjoy beer
Make more beer