First you need to understand what partitioning is. Partitioning is taking a single hard drive, physical drive, and separating it out into two or more 'logical' drives. This essentially makes your computer believe that there are now two hard drives in your computer. (It knows it's one separated but just play along). You want to install Windows on the main, or first, partition, your new C: Drive. When you install Windows 7, you can click on the Advanced button at drive selection time and then you can delete the partition, and create a new, smaller partition. You want to install Ubuntu (by burning the ISO to a disc and placing it in the drive) second as this will also install Grub, which is the nice little menu that lets you pick which Operating System to startup.
I haven't used EASEUS, but tomek claims that it may help with not losing your Windows files. This most likely partitions out your blank space into another drive so you never have to mess up the existing partition. I would defrag your drive before using it though as defragmentation usually puts all the files at the beginning of the drive leaving more partitionable space. (Yes, I know that's not a word)
To answer your question straight up, you have to burn the ISO to a disc and boot from it. You can also (if it's Ubuntu) just run it from Windows and install a copy "Inside Windows" as mentioned above and you can avoid this whole partitioning mess. If you're looking to use Ubuntu long term, then partition.