I followed the instructions for enabling the State and Country Picklist from https://resources.docs.salesforce.com/222/latest/en-us/sfdc/pdf/state_country_picklists_impl_guide.pdf
And afterwards when creating a new account records from the account objects, I can confirm that the State and Country Picklist functionality is working.
However I am not quite understanding how to access the feature on a custom object. As a test example I'd like to create an object that represents a candidate for a recruiting application but when I create the object and try to add a picklist field to add where the candidate is from, there is no difference in picklist options prior to enabling it.