How can I build a simple USB signalling device?
ATTiny + V-USB acting as HID keyboard. ATMega32U4 (e.g. Arduino Leonardo) acting as HID keyboard. PIC18F14K50 acting as, yes a USB HID device. There are a host of other USB enabled microcontrollers, those are just three I can think of off the top of my head.

You will need some microcontroller of some description capable of interfacing with USB. You can't just cut the end of the cable and hope to simply connect the wires together and get it to print numbers without some form of processor.

USB is a fairly complex protocol, so the best bet is to find something that will either do what you want (like a keyboard), or a microcontroller with a prewritten USB HID stack which you can then customise the code for to send key press info when a push button is pressed.

There are certainly sample codes available for the Leonardo board which can be used to send keystrokes to the PC.