I am go into to assume that you are using Windows.
First I would like to recommend Linux Mint 9 to you as it is one of the easiest distros to use. http://www.linuxmint.com/
I would also recommend the Gnome (which is a Desktop Environment) to start with: http://www.linuxmint.com/download.php , When looking at the download page, you will see that there is a LiveCD and LiveDVD 32-bit and 64-bit. If you don't know what your processor is then just download the 32-bit. The LiveDVD just has the program Java in it which is not really needed. If you download the LiveCD then you will need a 700MB CD-R/CD+R (doesn't matter if it is -r or +r), and a regular single layer DVD will work fine for the LiveDVD.
Download the ISO image (when you click on either the 32-bit or 64-bit it will take you to a different page where you can use the torrent or scroll down and click on the mirror link that is closest to you location).
Use a Program to burn the iso image (such as nero) if you don't have one I recommend http://infrarecorder.org/ which is Open Source (free). Download Infrarecorder and install, then start the program "Infrarecorder."
In Infrarecorder the first thing that is going to come up is a window with like 6 buttons, one labeled "write image," click it. A different window will pop up, search for the iso file, select it and click on the open button. Change the write speed to the slowest setting 1x if possible. Click OK to start the burn process.
Next if you want to test Linux Mint before completely installing over Windows, install it through windows. Double click on the CD icon in "My computer." Just follow the instructions from there.
If you choose to install completely:
Place the CD in the tray and reboot the computer, (you may need to alter your bios settings. Most newer system will allow you to hit the F12 key right when the computer reboots to load up a boot menu, if you are able to do this boot into the CD/DVD ROM. If not hit the F2 key to enter into the Bios and cycle through until you find boot properties, and make the CD/DVD ROM the primary, exit and save. Then let it boot into the CD/DVD)
This may not make sense with you reading this now but when you see it, it will make more sense.
*Select the first selection from the grub, with is boot into Linux Mint 9. Wait a while and let it load into the LiveCD.
On the Desktop you will see and Icon that is labeled Install. Double Click it and follow the instructions.
For a more advanced setup with the partitions see : http://www.youtube.com/watch?v=mSIZT-4sdc0
If you require more assistance you can send me an email.