What is the current version ?
You can find the current version of the system from the Admin -> System -> System Information.
Upgrade depends on if the website has been customised ? Or does the website use any plugins ?
If not then then just get the new version of nopCommerce and upgrade the database.
If the website has been customised. The website is probably running on a server then most likely that is just the binary files and does not include the source code. The original source code is usually kept on a separate development computer. That could be in house or maybe an external developer set it up and they have the source code.
In addition to Yidna's answer, I believe NopCommerce upgrades need to be completed in sequence version by version.
So if you running version 3.9, you would need to upgrade to version 4.00, then 4.10, them 4.20