If you hope to install any linux system to this hard drive, you will have to create some free space. It appears you do not have much space on C: D: or E: First task is to get rid of what you do not need.
If you need it all, then I would suggest you get your self a used system, and install a distro on it. You did not say if this is a laptop or desktop. If it is a desktop, you could always add a disk. That is the best solution, and leave this drive alone.
Beyond clearing some space, you will have to re-partition. I do not know what H: is used for. It appears empty. Is that the case, or is this some kind of recovery partition? You might have to look at the doc that came with the system, you do have it don't you?
Now, some concepts. There are several kinds of partitions. Primary, extended etc. A lot of manufacturers create four primary partitions, on laptops. If that is the case, you can not create another partition. Well, you can, by deleting a partition, creating free space, and then creating a extended partition, and then create partitions within the extended.
If you want to install to this HD, that is probably what you will need to do. H: is a candidate, if you can live without it. It all depends on what is on it. You will have to tell us that.
Now if you can delete or move data off D: and E:, you have the possibility to shrink them. You can shirk windoze parts with windbloze tools that are built in. That will help create free space. Just remember max 4 primary partitions, it does not matter how big the disk is.
Once you create an extended partition, then you could install linux there. You will have to set up dual boot. This can be done. I'm not sure whether FC15 uses Grub or Grub2. Either way, it can be set up so windoze will boot, and linux will boot. Before you attempts this, read and understand Dual Booting. It get more nobs into trouble than anything else. Grub will replace the windoze boot record, and replace it with Grub stuff. Many nobs mess this up, and find out after there linux install they can no longer boot windoze. So, be prepared.
Now for tools to do the partitioning. I have never used FC. Most distros do supply partitioning tools that you access during install. They can deleted partitions, and create new ones. If you mess with windoze parts, use windoze tools.
Linux uses different ways of refering to HD partitions. The first HD is usually sda, the second HD is sdb and do on. The partitions are sda1 sda2 sda3 etc. That is a very simple explanation, just to give you an idea.
For any linux install, I suggest you create a root partition, of about 10 gig. This is where the OS goes. Then create a small swap partition. If you have a gig of more of ram, you can create a swap of say 100 meg, 200 meg if you are nervous. On my 3 gig ram system linux has never used the swap. In fact with 3 gig of ram you are safe enough to not create a swap. The next partition is for home, this is where all your user stuff goes. It can be as big as you have space for. 10 gig is enough to get started.
I would also suggest you do some looking for a FC install HowTo document, and read it before you start.
Hope this helps, ask questions if you need to.