I'm Miles from the Social Care team at Shopify. Thanks for your question.
At this stage, Shopify Payments is not available for Faroe Islands. Shopify Payments is only available to select countries at this stage, but we are working on bringing it to more regions as time goes on. Faroe Islands has some great alternative options, though! You can check out a full list of available gateways in your country here: https://bit.ly/3ibqQ4t.
Shopify supports two different types of credit card payment providers: direct providers and external providers. If you're using a direct provider, your customers can complete their purchases directly on your online store without having to pay at a third-party checkout. If you're using an external provider, your customers must complete their purchases on a checkout page that's hosted outside of your online store. We also have a great guide to help you understand direct and external credit card payment providers a bit better. Once you're set up with a payment provider you'll be ready to take payment from your customers.
Once you've got your provider all set up, make sure you test your checkout to ensure everything is working. Each provider will have a different way of doing this, so be sure to check with them on how you can test transactions. We have a great guide to start you off with testing your payments: https://bit.ly/3n1QOuP.
We're here 24/7 to support you, so be sure to reach out if you have any other questions.