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 "My Registered Domains"
3) Click on the domain name you wish to modify. This should take you to a new page.
4) Go to "Set Up DNS Record"
There, remove the records with the following host / type combinations:
Host: www
Type: A
Host: @
Type: A
You can then add the DNS records specified by Shopify using the empty spaces at the bottom of the DNS records list:
Host: @
Type: A
Content: 23.227.38.65
Host: www
Type: CNAME
Content: shops.myshopify.com.
Once this is done, you can verify your connection at Shopify to complete the setup process.
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.