Sitecore Version Upgrade

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