Well, let's see.
Firstly, and unfortunately, not every machine will run Linux. So the first thing for you to do is get a "LiveCD" (Ubuntu runs as a LiveCD) Instead of installing, or "trying to install" the OS is loaded into system memory and it runs from there and the CD, with programs that you call for being uncompressed and loaded into memory from the CD. The Live CD does everything that a complete install would do, albeit much slower as you are limited by the CD read speed.
But this will tell you if your machine will even "run" Linux. If it does, and you like the looks of the Ubuntu interface, then you reboot the CD and do an install. This IS NOT something that Windows has anything to do with, and you don't install anything into your Windows partition in order to manipulate stuff.
There are many LiveCD's that you can try if Ubuntu won't run, or you don't like it. Couple of my favorites are PCLos and Mandriva One. I've not tried it, but SLAX seems to be the most popular LiveCD.
So if you go to install, always select "custom partitioning" Don't just let the installer fly as it can use your entire hard drive and it will overwrite Windows with the same lack of respect that Windows gives Linux.
In the custom partitioning window, you'll clearly see your windows partitions, and you can even resize them from here.
You need to create three new Linux partitions: first a "root" drive (shown as"/") where all the system files are installed, a "swap" file that you just 'create' without formating. Your swap file should be twice the size of your system's RAM. Oh, the root partition can be as small as 4 gigs up to maybe ten or so, won't need much bigger than that. Lastly you create a "/home" partition; that is where all your files like downloads and anything else you create will go. The system also stores your "user" files there too. Depending on the size of your hard drive 5-10 is ample, but make it as large as you like.
Format the root and home partition as "ext3" until you learn enough about Linux that you have reason to use a different file system.
Nice thing about modern Linux OS's is that they can read and write to Window's NTFS file systems, (FAT32 has been available for Linux for a few years) so that you can see and use your entire hard drive while using Linux.
That should get you started. If you get stuck, just hollar.
Most people find installing Linus these days to be much easier than installing Windows. So don't be afraid, and have fun.
Tom