Important
Do not go further if you haven’t made a backup of your shop. Rollback will be the only way to go back if something does not go well, and this requires a backup. Learn how to backup your shop
There are a few ways of upgrading the PrestaShop store. This chapter provides information about two methods of getting the software to the latest version.
You can use provided autoupgrade module to upgrade your store to the newest version using web interface. You can read more about the module and how to use it here.
Upgrade assistant module (autoupgrade) is fully accessible through cli. You can read all the details here.
Doing an upgrade by yourself can be risky. If you feel uncomfortable with doing it on your own, you can find support on prestashop-project.org.
Basically, the process and the result will be the same. The existing data on the shop will be kept, as well as your module and your current theme.
Many agencies and freelancers in your area may also provide this kind of service.
More information about support: PrestaShop project support page