Backing up computer before upgrading OSx

Question

should you backup your computer before upgrading and installing software (from OSx 10.5.8 to 10.6 snow leopard)

Answer 1

Yes. In fact you should always maintain current backups in case of a disaster. I recommend in this case you make a basic clone using the Restore option of Disk Utility.
Clone using Restore Option of Disk Utility
  1. Open Disk Utility in the Utilities folder.
  2. Select the destination volume from the left side list.
  3. Click on the Restore tab in the DU main window.
  4. Select the destination volume from the left side list and drag
       it to the Destination entry field.
  5. Select the source volume from the left side list and drag it to
      the Source entry field.
  6. Double-check you got it right, then click on the Restore button.
Destination means the external backup drive. Source means the internal startup drive.
Upgrading to Snow Leopard
You can purchase Snow Leopard through the Apple Store: Mac OS X 10.6 Snow Leopard - Apple Store (U.S.). The price is $19.99 plus tax. You will be sent physical media by mail after placing your order.
After you install Snow Leopard you will have to download and install the Mac OS X 10.6.8 Update Combo v1.1 to update Snow Leopard to 10.6.8 and give you access to the App Store. Access to the App Store enables you to download Mavericks if your computer meets the requirements.
     Snow Leopard General Requirements
       1. Mac computer with an Intel processor
       2. 1GB of memory
       3. 5GB of available disk space
       4. DVD drive for installation
       5. Some features require a compatible Internet service provider;
           fees may apply.
       6. Some features require Apple’s iCloud services; fees and
           terms apply.