I've made a two-stage rocket from scrap materials before, but that used gap staging (the hot gases from the first motor travel up to and ignite the second stage). That only works for smaller rockets, so this larger high-power rocket needed a different staging method: There would be electronics in the upper stage that would ignite the upper stage motor at the right time, separating the two stages. The first stage would then deploy a parachute, while the second stage flew on. Here's how I did it:

• In the upper stage, I made a compartment for the electronics, which would be an altimeter and a battery. This compartment only takes up half of the diameter within the tube, as the other half is for the upper motor's ejection charge to deploy the parachute. 

• From the electronics bay, a straw goes down all the way to the upper-stage motor. An igniter goes down this straw, with the other end attached to the altimeter. After a predetermined time after launch, the altimeter will ignite the motor.

• Just in case the motor is not able to deploy the parachute, the altimeter will set off an ejection charge at apogee (the peak of the rocket's flight), which will eject the parachute if the motor was not able to.

• The first stage's parachute will be deployed via the ejection charge of the first stage-motor. This will happen after the two stages separate.