Here is basic tutorial how to perform upgrades since 1.16 version. This version has different structure than old versions.

1. Read new version announcement article for any possible changes in settings/settings.ini.php. If article does not mention anything you do not have to do anything.
2. Disable cache in settings/settings.ini.php
   1. 'templatecache' => false,
      'templatecompile' => false,
      'modulecompile' => false,  
3. Write down what's the latest files from doc/update_db/update_<update_number>.sql
   1. If you are running 1.84>= you can easily find files which you have to execute in "Configuration" => "Update information" right side will contains links to files which you have to execute. You can execute these files content in any mysql management console. phpmyadmin, adminer and so on.
4. Overwrite doc,ezcomponents,lib,modules,pos,translations
5. Overwrite design folders
   1. design/defaulttheme
   2. design/backendtheme
6. Check that you have latest database updates from doc folder. You will know which files you have to execute based on your latest written file. You can execute database in your php my admin tool.
   1. You can skip this step if you have already done this based on "Update information" information.
7. Clean cache System configuration -> Clear Cache
8. Enable cache
   1. 'templatecache' => true,
      'templatecompile' => true,
      'modulecompile' => true,  

In all cases I suggest make backup.

Since 1.83 version you have to be running min 5.3 PHP version.