If your "Start" button at the lower-left hand corner is a blue Windows logo, then you have either Windows Vista or Windows 7. If not, you have Windows XP (unless your computer is older than 8 or 9 years old).
If your "Show Desktop" button is in the lower-right hand corner instead of the lower-left, you have Windows 7.
If you click "Start" and you have a "Search for programs and files" bar, you have Vista or 7. Type winver in that search box and press Enter. That'll tell you for sure which version of Windows you're running.
You can download IE8 via Firefox. You don't even have to wipe it out through "Add/Remove Programs" (XP) or "Programs and Features" (Vista*).
*: Although 7 has "Programs and Features," that's irrelevant for our purposes, as it has IE8 by default.