First things first, we have to get some kind of operating system running so we can use our Raspberry Pi. I chose Raspbian because it has hard float, is recommended by the Raspberry Pi Foundation, and (this was the clincher) because portmanteaus make me smile (I am an English major after all). If you are a complete and total noob, then it might be easier to buy an SD card with Raspbian (or one of the other operating systems) already installed. If you'd like to know how to make your own, though, here is a step-by-step.
Step 1: Download the latest Raspbian version from here:
2012-09-18-wheezy-raspbian.zip for me).
Step 2: I'm going to assume that most noobs will be running windows on their home machine, and thus will need to download and unzip Win32DiskImager.
Step 3: Insert a blank compatible SD card in your SD card reader, open up Win32DiskImager, and select the image you downloaded in step 1 (it should automatically select your SD card as the write destination).
Step 4: Click the "Write" button.
Step 5: Wait (patiently or impatiently) for your SD card to finish writing.
Step 6: Eject it from your SD card reader, insert it in your (unpowered) Raspberry Pi, then connect everything up and go!
Step 7: Set Up.