Once you've got all of youre equipment sanitized, you're ready to start! In the case of an extract kit, you're going to want a brew kettle approximately 2 1/2 - 3 gallons large. You're going to fill it with 1 1/2 - 2 gallons of water (depending on the size of your kettle), and bring it to ~150 degrees. Once you've gotten it to that point, you're going to start the "steeping" phase. This is where we're going to treat the steeping grains like a tea bag. You're going to put your grains into the steeping bag, and steep them in the water for 15-30 minutes. I've found that the latter of the two gives me the best results. While the grains are steeping, maintain the water at 150 degrees. You can poke the grains with your spoon throughout the phase for better results.
Once you're done steeping, try to drain as much of the water back into your brew kettle as possible, and bring the water to a boil. Once it's at a boil, you're going to add your extracts, both LME and DME (Liquid Malt Extract and Dehydrated malt extract) to the wort (at this point, you've now got "wort") and stir them in.
Once your malts are dissolved, and you're water is boiling, you're going to start the boil phase. This is where you're going to boil the water for ~1 hour, and add your hops. Depending on your kit, you're going to add the hops throughout this phase. Read the instructions on your particular kit for particulars. The hops added towards the begining of the boil will be your bittering hops, and those at the end are the "aroma" hops.
While your wort is boiling, add 2-3 gallons of water (depending on how much is in your kettle) to your fermenter, this will make things easier when it comes time to add your wort.
Once the hour boil is up, you're going to want to cool your kettle to some extent. I recommend filling a tub with cold water, and setting the kettle in there to let it cool. Once the wort has reached ~90 degrees, you should be ok to pitch it. Add your wort to your fermentation vessel, and then stir your wort very well. You want to expose as much of the wort as possible to oxygen, as the yeast will require it to reproduce, and make that beautiful beverage we all love (beer, you idiots :P ).
At this point, you can take a gravity reading if you like. This step is NOT necessary, and you shouldn't worry about what the reading says, it will not effect your brew in any way shape or form, just will give you an idea of what the abv and abw will be.
Read this thread if you have any particular questions about why the readings are unimportant:
Now you're ready to start brewing. Add your yeast (there are numerous threads dedicated JUST to yeast, you can search, or this one will outline preferences and has quite a few of the differences: http://www.homebrewtalk.com/showthread.php?t=643
) and seal your vesel with an airlock.
Now it's time to wait! As Charlie says, sit back, relax, have a home brew! There is NO set time for how long you should wait until either a) transferring to a secondary fermenter or b)bottling (if you're not doing a secondary) it's all relevant to your brew, the temperature, and numerous other things.
The next section will start out with when to transfer.