There's no good short answer to that question, but here's a short answer that isn't terrible:
With the sweep set to, say, 2mS/Div: if you get a fuzzy trace with no input signal to the amp, and you speed up the sweep--adjusting the vertical gain as necessary--and see a periodic rather than a random (noise) signal, your amplifier is oscillating at HF. If you have to slow down the sweep, you have LF oscillation (or hum).
Sometimes an amplifier will only oscillate when a stimulus (input signal) is applied, and this can show up as fuzziness, bumpiness or "squeeging" superimposed on the output signal.
Sometimes bad grounding in your test setup can produce the above symptoms (and others) as seen on the scope, even when the amplifier is actually working as it should.
This is not easy to describe verbally. But with some experience, you'll know it right away when you see it.