I presume that you're talking about a Windows Home Server v1 system, rather than one running the newly released Windows Home Server 2011, as these work very differently as far as recovery goes? I have swapped the system drive on my WHSv1 more than once without losing any of my data in the pool (and while keeping the majority of my machine backups as well).
The first important question is, did they have data duplication enabled on all of their shares? If they didn't then there is a large possibility that there may have been data that was only stored on the system drive, and was never duplicated on any of the surviving disks, so it won't come back unless you find some way to resurrect the old drive.
The basic way that you replace the drive is to pull out the dead hard drive, and put the new system drive in (same slot and connection as the previous system drive) and then reinstall the WHS OS (the way you do this will differ depending on whether it's an OEM built server that will generally come with some form of recovery disk, or a self-built/custom server that you'll need to redo from the install CD). If doing a "from the CD" install, ensure that you tell it you're doing a "Server Reinstall" not a "New Install". During the reinstall WHS will scan the other hard drives in the system, and will discover the old data and build new tombstone files for that data and set the shares it finds up again.
Finally once the server's built you will need to uninstall the WHS connector from your main PC, and then reinstall the connector so that it will go through the initial server setup wizard and let you name your server and apply the registration key.
See this for more info Setup: How to replace system drive and how Windows Home Server handles the primary hard drive