From Shopify Wiki
1. Log in to your Network Solutions control panel
2. Goto Domains / Manage Domains
3. Select your domain by checking the box next to it and click "Edit DNS"
4. Under "Advanced DNS Manager" click "Manage DNS Records"
NOTE - You are unable to add your CNAME records with Network Solutions Default A Records in place so you must first scrap your A Records. If something goes horribly wrong, you can reset to default afterwords.
5. Edit your A records and Delete @none, * and WWW records
6. Now return to the "Advanced DNS Manager"
7. Under "Host Aliases" click "add/edit"
8. Important! Under Alias, in an empty box put www | Leave the first drop down blank | Select the second radio button | In the Other Host box enter your xxxxx.myshopify.com (Note there is no . at the end like regular CNAMES) Important! Change xxxxx in xxxxx.myshopify.com to your actual store name...
9. You can also add another CNAME Alias for * if you are feeling frisky. Just repeat the steps above replacing www with *
10. Now click go
11. Now go to your Shopify store and edit your DNS & Domain name settings
12. Click "I would like to claim another Hostname… "
13. Enter your domain ie. www.myphatstore.com
May take a while to kick in so be patient.
If you run into any trouble, you will find it more helpful to first contact Network Solutions for support as they have access to those settings (while Shopify doesn't). Here is a direct link to their support page.