1. Decide the Target Sitecore Version that you want.
  2. Check if you have its pre-requisite version.
  3. Backup your Application and Database.
  4. Check which version you are currently on and what target version
  5. Execute the Pre-Install Database Script (SQL or Oracle, depends upon which Database System you use) if any.
  6. Install the Sitecore Upgrade Package.
  7. Execute the Post-Install Database Script if any.
  8. Check that your solution is working fine — Some level of regression testing.
  9. Make all the required changes to your custom code if it has stopped working
  10. After you test it throughly, build your solution again and deploy the latest build onto your Environment.

Sitecore CMS 6.4.1 Update rev.120113 (6.4.1 Update-6)

Sitecore Version Upgrade Tips - Part 1

Sitecore Version Upgrade Tips - Part 2