Easiest way to get running with Linux on your Raspberry Pi, is by downloading the NOOBS file from the Raspberry Pi website.
I picked the "Network and Offline" version (1.1Gb) since the other version didn't really do much.
After booting you can pick your distro of choice, Raspbian is probably the best choice for beginners.
1. Insert an SD card that is 4GB or greater in size into your computer.
2. Format the SD card using the platform-specific instructions below:
a. Windows
i. Download the SD Association's Formatting Tool from here.
ii. Install and run the Formatting Tool on your machine
iii. Set "FORMAT SIZE ADJUSTMENT" option to "ON" in the "Options" menu
iv. Check that the SD card you inserted matches the one selected by the Tool
v. Click the "Format" button
b. Mac
i. Download the SD Association's Formatting Tool from here.
ii. Install and run the Formatting Tool on your machine
iii. Select "Overwrite Format" (note that Quick format works as well if your SD was already FAT32/MS-DOS formatted)
iv. Check that the SD card you inserted matches the one selected by the Tool
v. Click the "Format" button
c. Linux
i. We recommend using gparted (or the command line version parted)
ii. Format the entire disk as FAT
3. Extract the files contained from the NOOBS zip file.
4. Copy the extracted files on your SD card (if the archive was unzipped in a folder: copy all files in the folder to the SD card)
5. Insert the SD card into your Pi and connect the power supply.
If you don't see anything on your monitor, press the 1 to 4 keys to switch video mode!
After booting your Raspberry Pi, the SD card will be "fixed" to the correct file system and you'll be asked which OS you'd like to use. Raspbian (Debian version for the Raspberry Pi) works best for beginners, but the other ones are most certainly worth it as well. (I run OpenElec on a Raspberry Pi for use with XBMC)