How can I copy my OS X to an external hard drive, so I may use the USB hard drive to start up my daughter's MacBook?
Her MacBook will not boot up, but instead shows a solid blue screen.
Either one of these will create an exact copy of your harddrive to an external. Then you can use the external drive to boot up the other machine.
You can not copy just OS X to a hard drive and install it to another machine. You will need your original OS X DVD for that.