Written Tutorial: https://learn.sparkfun.com/tutorials/how-to-use-an-oscilloscope?_ga=1.171970599.529458105.1355161158
100MHz Digital Storage Oscilloscope - GA1102CAL: https://www.sparkfun.com/products/11766
Digital Oscilloscope DIY Kit: https://www.sparkfun.com/products/12848
Digilent Analog Discovery 2: https://www.sparkfun.com/products/13929
USB Oscilloscope - MSO-28: https://www.sparkfun.com/products/11219
DSO Quad - Pocket Digital Oscilloscope (Black): https://www.sparkfun.com/products/12065
Oscilloscopes allow you to visualize how electrical signals change over time. This means you can measure periodic and transient signals, which might be too fast for your digital multimeter to catch. Oscilloscopes can be indispensable for debugging circuits.
In the video, I talk about why 10x probes are useful, how to tune the compensation capacitor in a 10x probe, how to measure periodic signals, and how to set up a single capture trigger for a transient signal. I hope that this works as a starting place for someone who might be just beginning with oscilloscopes.