I am upgrading my computer from leopard to snow leopard. Is it necessary that I back up? I'm afraid I will lose all my data.
I think you just answered your own question.
You should purchase an external hard drive.
I dont even know how to use Time Machine...
See the Setting up Time Machine backups using an external drive section here.
Go out and buy one. You should have a backup.
To upgrade you don't need a backup, but if the upgrade goes awry then what? You've got nothing but a ocmputer that doesn't work. Now you must erase the drive and restore everything from scratch. And, all your data are gone. Is that all worth the risk?
If you choose not to make a backup then at least do this before installing Snow Leopard:
Repair the Hard Drive and Permissions
Boot from your Leopard Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer.
If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
Now, boot from the Snow Leopard DVD and install it.