I assume that you have ALL of your data backed up.
I also assume that you have no other drives attached (external HDD, flash drive, SD card, etc).
Boot from the Ubuntu DVD, and select "Try without installing"
When everything loads, open a terminal and type:
If it was a Windows install, you should see 2 partitions: one for the Windows bootloader, and one for Windows itself. Delete both of these.
Now start the installation process. There should be an installer icon on the desktop.
When you get to the part where you choose between "Install Ubuntu xx.xx" or "Something Else," choose "Something else." When the partitioning menu appears, make a swap partition first, and put it at the end of the free space. I've heard all kinds of ranges for what size the swap should be, but twice your RAM seems to be a common suggestion (but see below for my personal opinion). Once you do that, make an ext4 partition. (If you have an SSD, choose ext2.) Make sure that the mount point is "/"
Now you can continue the installation like normal.
About the swap size: I hear "twice your RAM" a lot, but don't completely understand it. For example, say you have 256 MB of RAM. To me, it sounds like you'd want more than 512 MB of swap, but then again I don't know that much about how everything fits together.