Place a dispenser
Put one item in the dispenser
Place a comparator facing out from the dispenser
Place redstone dust from the comparator output
Add a redstone lamp or output line to read the signal
Power the dispenser with a button, lever, or pulse
Use the comparator output as the random result
For multiple outcomes, use different item counts in the dispenser
For a stronger randomizer, connect several dispensers to separate outputs
For a faster random pulse, use a hopper clock or observer pulse to trigger the dispenser