Laser Alarm Clock

The problem is, we don't know what type of hardware to use for the laser pointer to be shot at.

A phototransitor. Try to find one that matches the wavelength of the laser.

You'll have to experiment with resistor values, etc. to get the sensitivity right. You'll need to block ambient light as much as possible. You may need to an optical filter because it will be sensitive to light at other wavelengths... It's just most sensitive at the specified wavelength. If you need it to be completely immune to false triggering, you'll need a laser that can transmit a "code" similar to the way a remote control works.