Dolphin is a complex platform. Boonex provides a way to upgrade safely. However, you do have to prepare. First step is to backup your Dolphin database and your Dolphin site files. The upgrade script will be making changes to both so just in case something goes wrong, you will have a way to recover your site.
Then you simply upload the Dolphin files from the upgrade to your site. Remove the .htaccess file from the upgrade directory/folder and then point your site to http://mydolphinsite/upgrade and follow the instructions.
The 7.3.1 upgrade is a simple one that only makes a few changes which makes it a good one to learn on. I still recommend backing up everything first.