Alrighty, I'll take a shot at this. 5 easy steps:
1. Connect your hard drive and go into Disk Utility. Click on your hard drive's main heading, not the secondary name.
2. Click on the Partition tab. You'll now see your hard drive represented by a picture. The used portion of it will be blued out.
3. Click the plus [+] sign at the bottom. You will see your hard drive split into two parts…
4. Put your cursor over the mid-section between the two partitions and drag it either way to make either side bigger or smaller. Just don't drag this into the used portion (I don't think you can) and it won't get damaged or erased.
5. Click apply and your new partition is formatted (Name accordingly first, if you don't like the name selected for you).
Name this portion "backup" or whatever and select this "disk" when creating your Time Machine backup.
For the record, I don't recommend doing it this way. HDDs are cheap, so if you can swing it, I recommend having one clean HD for backup and one for big data (like movies) which balloon too much to keep on your small Mac HD. Good luck!