There are two ways you can assign a domain to your shop. The question is, if you want to use the domain for anything else than your store. If you would like to use it for anything else such as email or creating a subdomain, you should rather point it to our cname. If it will be used for the shop and email, the simplest way would be to point it to our name servers (Ashop hosts the domain).
If you would like to create cname record, this is what you should point it to:
This should be done from your hosting company admin panel.
If you want to point it to our nameservers, here are the addresses for those:
This should be done from your domain registry admin panel.
After you point the domain to your store, I would advise waiting a few hours for the change to go through. It might take up to 48 hours but usually it takes a lot less time, maybe 2 hours. Then add your domain in your store admin panel. You can do that in Settings -> Domain & Email Management -> Domain Names -> Add New Domain in the top left corner. The are instructions on that page. This will only work once the change has gone through. If you get an error, please wait a couple more hours.