To install a distribution that needs access to the source medium while running, then you will need to do the repartitioning before you launch the actual installer.
Repartitioning using Parted Magic
First, start UNetbootin, and use the Hard Disk install mode to install Parted Magic. Reboot, and select the UNetbootin boot option to boot into Parted Magic. Launch the partitioner from Parted Magic, and shrink your Windows partition (remember to resize, rather than delete, your Windows partition, even if you don't want to dual-boot, as you will need something for UNetbootin to run from; you can delete it later). Now you will have some free space left for Linux; leave it as-is, as most user-friendly installers (such as Ubuntu and Fedora's) will automatically create partitions in the free space appropriately.
Making a frugal install of your installer
Next, boot back into Windows, and run UNetbootin again; it will prompt you to uninstall the Parted Magic install, and say yes. Next, start UNetbootin again, and again using the Hard Disk install mode, supply the iso file you wish to install (such as the Ubuntu desktop iso). Now reboot again, and select the UNetbootin boot option to boot into your frugal install's live environment.
Performing the actual install from the live environment
Now that you're booted into the live environment, launch the installer (on Ubuntu and Fedora, it's an icon on the desktop). Go through the steps as usual, but when you get to the partitioning stage, make sure that it's using the free space that you previously set aside for Linux, rather than attempting to resize any partitions.
Cleaning Up
Now that you have a full, standard install, you can get rid of the frugal install you used to launch the installer from; just boot Windows and uninstall UNetbootin.