Download the image:

First step would of course be that to choose and install a linux distribution on the SD card.
I'm personally a RedHat/Fedora user since quite some time but I thought, for the RasPi, to give Debian a go. I decided to install Raspbian “wheezy”, an optimised version of Debian for the Raspberry Pi, and it comes with LXDE as default desktop environment, for those who care about it.
You can download the image from the RaspberryPi Downloads page.

Write the image on the SD card:

The Raspbian image, and most likely that of other distributions, comes in some sort of zipped archive, being it zip, gzip, bzip2 and so on. So before proceeding, unzip the image with your tool of choice.

• Writing the image in Linux:

  To write the image in Linux, plug the SD card into the reader, or the SD-to-USB adapter and check the device node with:
  
  $ dmesg | tail

  That will give you the device node associated with the SD card.
  I assume here to obtain /dev/sdb as device node, and /dev/sdb1 as partition node.
  Be sure to unmount the partition before proceeding with the image writing.
  
  # umount /dev/sdb1

  Now to write the image onto the SD card, issue the following command:
  
  # dd bs=1M if=/path/to/the/image/file.img of=/dev/sdb

  Note that the dd command must be issued onto the device node, not onto the partition itself.
  At this point the image will be written to the SD card. Remember to sync any possible buffers with:
  
  $ sync

  When done, remove the SD card and you're ready to go.

• Writing the image in Windows:

  To write the image in Windows, simply download Win32DiskImager.
  Plug the SD and execute Win32DiskImager. It will let you select the image to write on the card, select the device to write the image to, and you're done.