Download and run UNetbootin. Choose the radio button next to "Disk Image." Select "ISO" from the drop-down menu next to that, and navigate to the location of the ISO file on the Ubuntu installation CD. At the bottom of the same dialog box, choose "USB Drive" from the drive type drop-down menu, and then select the USB drive's drive letter from the drop-down menu next to that. Click "OK."
Wait and watch while UNetbootin copies the files and installs the bootloader. Click "Reboot Now" when it is done.
Watch as your computer reboots and reads the Ubuntu files from the USB drive. If it boots back into Windows instead, reboot it and change the order of drives it boots from. At the beginning of the reboot, you will hear a beep. Press F2, F10, F12 or whichever key causes your computer to enter the BIOS setup. This varies by computer; you can use trial and error to find it or consult your computer's manual. Once in the BIOS setup, select Boot Sequence and specify that the computer should try booting from a USB drive before booting from the hard drive.
Explore Ubuntu. Once the computer is configured to boot from the USB flash drive, it will boot into Ubuntu. You can use the operating system and any files installed along with it. However, Ubuntu is not actually installed on your computer's hard drive at this point. If you want to go back to Windows, simply reboot the computer and remove the flash drive. Or you can click on "Install Ubuntu" and actually install Ubuntu on your computer's hard drive. Once you do this, it will write files to your hard drive and possibly erase data you have stored there, unless you choose the dual boot option.