You can see the CSS you are using in your Google Merchant Center account, or you can simply Google a product search and check the bottom of your Google shopping ad. The section where it says "By... ". For example if it says "By Google" you are using Google CSS.
If you are using our self service CSS it will say "By Moose"

Open "General account options" from the admin symbol in the top right corner

Open "Account settings" from the admin symbol in the top right corner.
You can also see your CSS in the top right corner

• Default in Google Merchant Center is Google’s own CSS
• You can switch to any other Google CSS Partner, such as Moose
• The CSS Partner will initiate a CSS transfer request in your Google Merchant Center
• Accept the transfer request in Merchant Center and you’re done
• Nothing else will change in your account or Google ads

When the Google CSS Partner has initiated the CSS switch you will se a request in your Google Merchant Center account.

Accept the request and it's done!
The switch can take up to 14 days depending on the grace period of the CSS you're leaving.
Google does not have a grace period, meaning if you switch from Google CSS it will take affect pretty much immediately.