There are a couple different ways to determine the technologies a site is using. Firstly, if you are technically savvy, you can right click on an eCommerce page (either catalog, checkout page, etc) and look at the source code. Many platforms will have hints in the source code that will give you an idea what the site is running.You can also look at the DNS/hosting information, which would help you determine if the eCommerce solution is hosted or SaaS (like Shopify, for example).
You can also try using InterNIC and enter the domain name. The results will return the nameservers which could point you in the right direction.
Finally, if all that sleuthing seems too difficult, there’s an easier way! Try BuiltWith. It’s generally pretty reliable, as long as the system you're looking up isn’t custom/proprietary. Enter a domain into BuiltWith and it will show you the platform, widgets used, analytics and tracking codes, CDNs, CMS, payment processors, and more.