We are a SAAS that host MS Dynamics for our clients. All of our servers, etc are hosted through an outside data center.
Currently our clients who sign up for hosted MS Dynamics are given a username and password by us. Some of these clients wish to integrate their AD with us, so their users who use our hosted MS Dynamics username and passwords are the same as their AD.
As Joseph has stated ADFS is the way to go with this. ADFS is a very involved process to setup / configure. Once you have this up and running it is fairly seamless to integrate with other clients/domains etc. Take a look at the below TechNet for additional information and also types of configuration that you can use to accommodate your existing environment .
https://technet.microsoft.com/en-ca/library/cc772593(v=ws.10).aspx
Will.