The schematic is showed next:

As you can see, the design is pretty forward: The pic18LF14k50 drives some NPN transistors, which allow the display to light. Same for the buzzer.

As you may know, the display has the four displays in parallel, so we will need to have a high frequency blink in order to "trick" the human eye to see them all light at the same time. 

For the buttons, a RC filter made of 10K resistor and 100nF will filter any bouncing effect, having a great counting experience.