My C drive is 20GB large and almost full, how do I regain space?

The story is pretty simple. Windows 7 Ultimate is about 10GB. If you have any backups, hibernation enabled, or pretty much anything, you won't have much space left. The only thing to do is get a bigger drive.

Sorry.

EDIT: To address the comment of the OP, if they are different physical drives, I would just install windows 7 on the largest one (if this will be your primary OS, else at least on something with about 50GB or so of free space).
If there is really only one drive, but it is partitioned, you can add space to your partition with drive management (just search for in the box on the pearl menu).

Here are two things that I usually do when I need disk space (I'm using W7UL with 40GB SSD):

1. Release disk space disabling your hibernation and delete hibernation file:

   Click on your Windows Start Button / Type "cmd" on the search box, then type powercfg -h off and press Enter (see screenshot below).

   

   This option will disable hibernation, delete the hiberfil.sys file, and remove the Allow hybrid sleep and Hibernate after Power Options under Sleep.

2. Use the Windows Disk Cleanup utility:

   Click on your Windows Start Button / All Programs / Accessories / System Tools / Disk Cleanup. Select what you want to clean and press OK. (I recommend you cleanup your temporary files included on one of the options). See the screenshot below:

   

Your hard drive just barely meets the minimum requirements for installation. Here are Microsoft's requirements for Windows 7. Simply put, you need more capacity.