Download http://unetbootin.sourceforge.net/to a computer and have a USB-stick memory ready.
Then just start the program, chose, for example, Xubuntu from the program options and the "14_04 live" version and let it install to the OS to the USB drive. Then boot the old computer from the USB drive. Either you can run the live version from the USB or you can install it to the harddrive on the computer. The latter is probably what you want if you intend to use the computer more than just testing it.