Let me try to condense this properly.
2 knobs to worry about on scope.
1. How tall the trace will be (vertical gain)
2. How fast the dot is travelling across the screen (horizontal sweep rate).
Now, with probe in hand, we take, for instance, a single stage common emitter circuit. We take our oscillator and feed a 1khz sine wave into the input connector.
Now we place our probe on the base of the transistor. We see a sine wave on the scope. We adjust the vertical gain to make the wave the correct height to view. We set the horizontal sweep rate to get the waveform to become, say, a single sine wave pattern.
Now, we make a mental note of how much electrical signal the sine wave is making, by looking at the scope's input setting.
We move the probe to the collector of the same circuit, and if the stage is working correctly, we should see the same waveform, except much taller.
We make a note of this scope setting also. By using the divisions on the scope screen, combined with the input switch settings, we can look at the trace and tell what the signal level is.
If the collector is not giving a taller signal, or is showing a sine wave with distortion or other imperfections, then your circuit be broke.
Good thing you have a scope, eh?