I like to draw out my circuits and then color over the lines after I’ve soldered them or re-checked them.

I really enjoyed this overview of electronics debugging made by MIT TA D. Elliott Williams:

Here is a summary of the main thinking as I see it:

-Circuits cannot be wrong, if there is a problem it is “either be because you do not understand what you built or you did not build what you understand.”

-You must first understand how a circuit works before you can debug it. If you are using components, understand the datasheets.

-To debug a circuit, first establish what it is doing, this narrows the list of possible errors down considerably.

-Think, what could cause this type of behaviour? Make a list of possible causes and cross them off one by one.

-Get a fresh pair of eyes on your problem.

-Systems are composed of sub-systems. Isolate sub-systems and test them each in isolation.

-Build your circuit neatly and logically, this makes it easy to check connections and reduces noise from entering long wires.

-Use the continuity mode on your multimeter to test connections.

-Make sure you are not misusing your oscilloscope (check the x1/x10, if in DC/AC coupling, that the ground clips are attached to ground, )

-Rebuild your circuit but with all different components on a different breadboard.