That is a good option if I cannot re-purpose this alarm clock, but I wanted to try and take something I already have and alter it.
Try take a ground wire and a 5V wire in series with a 300ohm or more resistor, use the ground wire and resistor to touch the connections to see if you can light up any of the leds. Might be fun. Just don't apply 5V and gnd directly to pins.
Use leads 1 and 2 to touch two pins on the display, hopefully you can find what goes on.
I would probably buy some similar displays that I know how to connect to them. Then make this known display work to get yourself some joy and confidence. Just don't be stuck on this unknown display and give up electronics based upon bad experience on the display