First, you have an instructor for a reason, so listen to him, not me!
But on a theoretical note:
Most of the responses have included "keep the nose on (or x fingers below) the horizon".
Hands off, a trimmed fixed wing aircraft will happily oscillate up and down swapping height and airspeed in a "phugoid" oscillation.
The oscillation period theoretically depends only on speed and is typically 20-30 seconds.
Confusingly, the pitch and vertical airspeed change fastest when the height and airspeed are not changing at all, and vice versa - trim actually keeps the angle of attack the same throughout!
This is why "chasing the needles" is a hard way out of the problem.
However, if you hold any sensible attitude at all vs the horizon, the vertical airspeed acts like a kind of friction.
This is because it changes the angle of attack so as to oppose the vertical motion, and damps the oscillation.
Theoretically the oscillation is damped away to "noise" in some 2-3 seconds.
Then you can fly the aeroplane again!
