If you're using Linux you're on your own I'm afraid - unless there's anyone reading that would care to share the power??!
On Windows it's easy - open MyComputer and right-click the drive allocated to the card. Select Format from the context menu. For the filesystem select FAT. Not FAT32, plain ol' FAT. Click start and a few seconds later you're done.
Now imagine how much data you're going to write. Find or create a 'donor' file on your harddrive. The contents are irrelevant - you'll be overwriting them. It's the size of the donor file which is important. Too small and you'll lose data 'off the end' when you read it back in the desktop computer. Once the donor file is ready, make sure it's named in 8.3 fashion and copy it to the card. Put the card to the arduino.
You can store whatever you like on the card. I recommend strings because they're the most portable format. Use DevicePrint and putting strings in the file is as easy as using the Serial.print functions.
Remember though: Every time the program runs it will start writing at the start of the file. If you don't want this to happen, then you'll have to think awhile and imagine a scheme to help!