Download the ISO file of the Ubuntu you want to install. I prefer to download using BitTorrent for speed and robustness.
Download and install the Linux Live USB Creator, also called LiLi. It is installed with the name LiLi USB Creator in the Windows Start menu or Start screen.
Plug in a USB flash drive of capacity 1GB or more. It should be mounted by Windows as a drive.
Run LiLi. Yes, it has a weird and funky GUI. Choose the USB drive and downloaded Ubuntu ISO file for installation. If the settings you chose are correct, you should be able to click the Lightning button at the bottom. LiLi should make a bootable Ubuntu installer on your USB flash drive.
Restart Windows and boot from the USB flash drive to install your Ubuntu.
Tried with: Windows 8 x64 and Ubuntu 12.04.2 LTS