If there is a new version available for your AbanteCart, you will have a notification in your message box of AbanteCart administration.
Download upgrade package
Download upgrade package from the AbanteCart Github releases page or for older versions Google Drive and http://sourceforge.net/projects/abantecart/files/
Back up AbanteCart database and code. There are several back-ups approaches The Backup Wizard interface in your hosting CPanel, AbanteCart built-in backup, Manually backup all AbanteCart files and MySQL Database via phpMyAdmin.
Decompress the upgrade package
Open the archive and copy all contents of "code" directory to your AbanteCart directory. You need to override directories and files if your copy process request confirmation.
Change MySQL database tables prefix
Open the upgrade.sql file in text editor and replace beginning of table names (prefix) "ac_" with your tables prefix selected at original installation. The easiest way to replace all "ac_" instances with your table prefix via your text editor's Find&Replace tool. To check prefix, you can open your database and check the beginning of all AbanteCart tables. If you did not use a prefix, replace with empty.
Run modified upgrade.sql
Run modified upgrade.sql file in MySQL (command line, phpMyAdmin or other )
If upgrade.php file present in upgrade archive
Finally include upgrade.php file somewhere in admin controller. Say in /folder_where_cart_installed/admin/controller/common/head.php in about line 30.
Load admin page once! This will execute PHP update script and will run commands from the upgrade.php file
Remove the include line.