If you have not already seen it, Shopify provides some instructions on connecting custom domains here
To make the DNS changes they require, you can edit DNS records through us (NOTE: If you are delegated to 3rd party nameservers then this change must be done from nameserver provider's side instead of us) -- to do this:
1) Log into your user account.
2) Go to "Domains" -> "My Domains"
3) Click on the domain name you wish to modify. This should take you to a new page.
4) Go to the "DNS Settings" tab
5) Select the "Use OnlyDomains Name Servers" option (If it isn't already selected) and click "Edit Zone Records"
There, remove the records with the following host / type combinations:
You can then add the DNS records specified by Shopify using the empty spaces at the bottom of the DNS records list:
Once this is done, you can verify your connection at Shopify to complete the setup process.
Please note that if your domain is not using our nameservers (has status "delegated"), the "Edit Zone Records" button will not be visible, and DNS changes would need to be made at the current nameserver provider.
Once the change is made, please allow up to 24-48 hours for the changes to be effective in all locations -- it usually takes effect within the day, however. People who have not visited it before will tend to see the changes much quicker than people who have visited the domain prior to making the change.