When I'm getting here:
The installer won't let me install because it doesn't determine the D: partition. It complains that there is not enough space on the C: partition.
How can I tell the installer to install on D:?
As pointed out, that part of the installer does not detect partitions.
Also, if you are going to install Ubuntu onto an empty partition, it is best to leave it unformatted, so that when the installer looks for free space, it will prefer the empty partition, instead of reporting all partitions as in use.
You can delete the "D:" partition from the Windows Disk Manager.
When you go on, you'll soon get to a screen that allows you to determine the partition where you'd like to install Ubuntu. It won't be called "C:" or "D:", but probably something like sdaX, where "X" is a number. If you have several partitions, it could be any number. Look for the partition (e.g. sda5) which is the size of what you think of as your "D:" partition; that's the one you want (as long as you don't have more than one partition of the same size!). Choose that one for the installation, and probably "/" for the mount point.