Install/running ubuntu on external HDD with a Windows laptop?

Yes, you need to install Ubuntu on the external drive. After that when you computer is booting, hit F8 or whatever gets you to the boot menu. If your laptop does not have a quick boot menu, than you can hit Delete to enter the bios setup. Change the boot order so the external is on the top of the list. There will also be CDROM and others. This menu tells the bios which device to try to boot first. I.e. If CDROM is at the top or has first priority than it will be checked first. If no boot media is found I.e No cd is in the drive, than the bios will check the second option on the list for some boot media. Note: Most computers have a quick boot menu by pressing a key in the bios start up (Usually F8). You will see the External in that menu by its' manufacturers name.