For rockets using the Estes-type (Black Powder) engines, one usually tapes the various stages' motors together (end-to-end). That way, the hot gases blowing through the booster's engine enters directly into the nozzle of the second stage's engine. Use Scotch Magic Transparent Tape (not masking tape), since it melts faster when the second stage ignites. and isn't thick.
If you want to use an existing single-stage rocket and make it able to handle a second stage, just make a booster stage. Your existing rocket will now be the "second stage," or "sustainer." The new booster stage that you'll make has no thrust ring, and it should be the same length as your booster engine. If you want to use an Estes E-impulse engine, you'll have to make the booster body tube longer than for A-D engines.
Make some large fins for your booster, and line them up directly underneath the sustainer's (2nd stage) fins. That way, you'll have good aerodynamics.
Select a zero-delay engine for your booster, such as a C6-0 or D12-0. As soon as the booster stops thrusting, it will "blow through" into the nozzle of the 2nd stage. The 2nd stage (sustainer) will ignite quickly, and the booster will tumble back to the earth. You don't need a parachute or streamer for the booster.