I was in this position a couple of years ago. My Acer Aspire 5000 laptop had a harddrive failure. I didn't have the cash for a new HDD. Plus I didn't have an actual OS to install if I did replace the HDD. So, what can I do for free?
Some of the best suggestions I read about getting started with Linux were to try Live CDs http://www.livecdlist.com/
. OK, so there is a cost of blank media
A live CD will not change anything on your current computer and will allow you to explore Linux at your leisure. I found a couple of distributions that I liked.
My next step was to move into the realm of installing Linux to a USB flash drive. This seemed more permanent. And would free my CD drive! I read a lot of instructions about how to do it manually, and it was
interesting to try that route. Today I use UNetbootin http://unetbootin.sourceforge.net/
to create bootable USB drive.
Eventually I could found a WD 320 GB MyBook at an end-of-year discount. I had been playing with Linux on CD or USB drive for a little over a year, and decided it was time to have something more permanent. I downloaded an iso marked as OS installation from the live CD list (I noticed at some point that all of the distros that I liked were related to Debian. Plug everything in, start the computer, and simply follow the on-screen instructions like any other OS install.
Note: Will your computer boot from USB? Most newer computers do. You check this in the bios. Move the 'Boot from USB' option to the top of the list. Also, if you have the original HDD and the USB external both installed, you'll want to know which one is which so you install to the right place. USB drives are recognized as SCSI. So, /dev/sda instead of /dev/hda.
Lastly, welcome to a different OS! Thanks for asking.