You can buy new domains through the builder area or point existing domains to your SimpleShop.
Pointing existing domains to your shop
To add a domain to your shop, you will need to ask your domain administrator to add a CNAME record pointing to custom.simpleshop.com for your "www" subdomain. You can use this tool to check that the records have been added: http://mxtoolbox.com/SuperTool.aspx
Once the CNAME record has been added, you can click the 'make default' button next to your favoured domain to ensure that it becomes the main domain for your shop.