Here's a few facts about this before getting started.
First, shrinking a hard drive only applies to Dynamically sizing disks. Since these do no shrink on their own (there's a lot of reasons why) but only grow, they might need to be compacted later to free up host space. It only reduces the .vhd file size by shrinking the 'shell' (if you will) to take up the drive space that is not being used by the guest OS.
In my situation, I was dealing with a drive that was not dynamically sizing but was static. If the vhd is static, the Compact button will not show up when you go to edit the drive.
In my case, I did not have to compact the drive. As I said, a drive cannot be compacted unless it is dynamic. Since mine was static, I converted it to dynamic to regain the compacting functionality but because of the way the conversion process works, it automatically 'compacts' the .vhd. My original static .vhd was 100 gigabytes. The output was 15.5 gigabytes.
Though I did not have to compact my .vhd because the conversion process did it for me, I'm going to put the instructions on how to compact the .vhd anyways.
For starters, the virtual machine that the hard drive is attached to must be turned off. Once the server is offline, from within the Hyper-V Manager (it's an mmc snap-in) go to the virtual machine's properties (right click the machine and select properties). Select the drive you want to shrink on the left panel that lists the various devices attached to the virtual machine. After selecting the drive, on the right panel, select Edit. This will bring up a window that tells you what editing a drive does and gives you the option to not show that screen again. Click Next. From here you should have three options (unless the .vhd is static). Select Compact and click Next. Finally, click Finish and Hyper-V Manager will shrink the .vhd as much as it can.
