How do clients map domains without cpanel

I'm having some issues figuring out how clients can map their domains to their pro site.

I've always done it in cpanel for all my sites by adding the domain as an aliases and everything works, but that won't work for this unless I have clients set their name servers to my server and I add them as an aliases manually and I don't want to do that much work. The point is to make the site run almost on its' own.

From what I understand I can have them do the following with their domain registrar and it should work:
Create 2 A Records:
website.com and http://www.website.com
TTL 14400
Address: 168.144.134.44 (my server IP)

I tried that and it did not work. Do I need to them to set their name servers to my name servers in addition to the A records or do they just need the A records?

The only other thing I can think of is that is the main IP address for my server and I do have other sites on the server. Do I need to get a 3rd IP just for the multi site install? (second IP is the secondary DNS ip)