LinkedIn has a nice introductory course for beginners using oscilloscopes (see below).
While the ubiquitous multimeter is useful for examining and debugging DC circuits, it has limits. For circuits that only have constant voltages that's usually OK, but for more complex circuits thoyou need to see the waveforms of voltages that change over time -maybe an audio signal playing music on a speaker.
An oscilloscope is just that it shows on its screen just how a voltage changes over time. It displays the measured signal with voltage on the vertical axis and time on the horizontal axis. Often the challenge is to know how to drive the scope so that it shows you clearly what's going on with your signal.
We have lots of introductory videos on our YouTube channel and plenty of entry-level scopes to choose from to buy.
If you're a beginner, or need the basics, take a look at this free LinkedIn course:
Electronics Foundation Course: Oscilloscopes http://bit.ly/2q2kbmt