That's a tall order! However, I will tell you that all IDE (SATA/PATA) hard drives only allow for up to 4 primary partitions. But you can have several "extended" partitions within any one primary. So if you need more than 4 partitions (and you probably will) you can do it by assigning at least one of your primary partitions to contain as many extended partitions as you like/need.
Windows and it's boot partition (the "System Reserved" one that's probably only 100Meg) will probably already be set as primary partitions. Do not change this unless you're willing to totally reinstall everything!!! It is possible to move everything in your "System Reserved" partition to your Windows (aka C:) drive or vice verse, but not without a whole lot of grief (and more partition adjusting). It's even easier when you install Windows since you can tell the Windows installer to not make this "System Reserved" partition but there's really no need to go changing things around now. Just leave it and the Windows (C:) alone.
The only monkey wrench in all this is your HP TOOLS partition. This thing is likely where your Windows (re)installation files are located. So if you delete this then you may not ever be able to reinstall Windows. You will need a Windows installation DVD if that ever happens. So you may want to back this partition up somehow and/or move it's contents somewhere else at least temporarily since you will probably need to do just that - delete the partition. Don't just copy this stuff either. Use a drive imaging program (not to be confused with graphics stuff either). This HP TOOLS partition might be entirely something else so don't hold me to that. I just know that many OEM companies like HP do provide a hidden partitions that contain all the Windows installation files as well as other stuff in the event that the computer needs it's OS reinstalled (which, in the case of Windows, is only a matter of time).
Now, you also need to understand about file systems too (since you asked). And as you may know, Windows 7 (Vista, XP, 2000) use the NTFS file system. Windows can also see and deal with the FATx (FAT32) file system too. But that's about it. Ubuntu and just about every other Linux distro can also see and use the NTFS/FAT file systems and others. But Windows can't see the file systems that Ubuntu normally uses. (At least, not easily.) Therefore, you will probably want to leave your shareable data on a NTFS or FAT prepared partition (drive). That way Windows and Ubuntu can both see and deal with it without too much trouble.
One other thing. When you go adjusting your partitions by shrinking something you run a huge risk of loosing stuff. Therefore, reduce your risk and defragment Windows - since that's the partition you will likely be shrinking. Defragging should be a normal habit and it's even scheduled to run in the background with Windows 7 assuming you haven't adjusted something. But background defragging will only deal with files - it's not a complete drive defrag. So do it! And don't say you weren't warned if you don't.
That's about the best "quick" advice I can offer. For more, check this out:
That said, are you sure you don't just want to run Ubuntu virtually?! It too can be a bit of a PITA to set up, but it's nowhere near as dangerous as messing with real partitions. If this sounds like a better plan then check this out:
Hope it helps. Good Luck.