I liken a discussion like this to, let's say, doing research on optics to be able to use eyeglasses. The scope is intended to be a tool to inspect the operation of electronic circuits. And so, one first needs to know something about the circuit being tested. One needs to write the equations, and draw the waveforms. Once you can do that, the scope merely verifies it. It will show, mostly, voltage in the vertical axis and time in the horizontal one. You need to adjust the sensitivity to get a display that fits nicely on the screen, and the sweep rate to get a display that shows a few cycles of operation.
In addition, the horizontal needs to be locked into the frequency of the circuit by means of its triggering controls. Most of the time you need to adjust the triggering to get a reliable trace or, failing that, go into automatic to let the horizontal sweep go by itself to get started in adjusting the trigger.
While this could be an oversimplification, it is complicated by the plethora of digital oscilloscopes, which aren't oscilloscopes at all, but computers that analyze a signal and then try to plot it on a monitor. Everything else is just bells and whistles to do a more in depth study of the wave.
So first, you need to be working with a repetitive signal, such as a sine wave from a generator. So you plug the generator into the scope and start monkeying with the controls to see what you can do. If the screen is blank, it's due either to the sweep not triggering or to an input signal so large it's off the screen. After some knob twisting one should finally see something and then see what the various controls do.