That fateful moment has come.  You've powered on your circuit, and it doesn't do what it was supposed to.  Now you've got to track down why there's a discrepancy.

Since the physical phenomena characterizing circuit behavior (voltage and current changes) are invisible to the eye, you have to rely on measurement tools (e.g. multimeters and oscilloscopes) to determine what's going happening.  This means that not only can there be problems in your circuit, but there may be problems with the observations you're making not aligning with what you'd like.

This happens to pretty much everyone sometimes when working with circuits. In fact, some ongoing research indicates that a common thread among faculty teaching electronics is the idea that “Nothing works the first time”.  However, if you work systematically you can save yourself a lot of grief when things go wrong.

General Strategies

There are some generic things you can do when you try and troubleshoot your circuit.

Measure something known

In order to test if your measurement equipment is behaving like you'd expect it to, try and measure a quantity that you're certain about.  For example, you might want to measure the fixed 5V supply to verify that a multimeter is working, or measure the current through a 1 k$\omega$ resistor when 5V is connected across it. 

  • If you don't see what you expect, then there is likely a problem with either your test device, your cables, or (possible) your connections.
    • Trying another test device can help in the first case
    • Swapping cables can help in the second
    • Reconstructing your test circuit or asking for a second opinion can help in the final case.
  • If you do see what you expect, then it is most likely that your measuring device works.  At that point, you should turn your attention to the rest of the circuit.

Simplify

If feasible, modify your setup to reduce its complexity.  You may try running fewer or shorter wires to make your board a little less cluttered and easier to follow.

Divide & Conquer

If you have a multi-stage circuit, take advantage of the 

When all else fails: Test the unexpected

If you have run out of reasonable paths of testing, try some less reasonable ones!  Does the problem change when applying pressure to any component? Does the physical position of the cables matter?  Does simply touching a part of the circuit affect the output unexpectedly?  

Note that unreasonable tests should serve as a last resort, otherwise you may end up following some relatively pointless leads (e.g. testing to see if your shirt color affects the circuit's behavior).