Fundamentally knowing when to use capacitors / inductors
The best way to visualize, without proper knowledge, is that a capacitor allows high frequency signals to pass through it. An inductor allows low frequency signals through.

Knowing this, you can use it in a circuit in the following ways:

Capacitor:


If you have unwanted noise (high frequency) on the power line going to an IC, you can put a cap in parallel to the IC. This will "let" high frequency noise go to ground instead of through the IC.
If you have a part switching on and off quickly, it wants to grab instantaneous current from the power line (high frequency). The power line will dip , which looks like a high frequency blip on the power line. The capacitor stops this by "giving" some if its stored charge to the IC until the power supply can catch up.
If you have unwanted DC voltage (low frequency), it will block the DC signal and only allow the AC/RF (high frequency) to go through. So, if you have an AC signal, you can put a series capacitor to make sure no DC goes through and hurts the rest of your circuit.


Inductor:


If you have unwanted noise, you can use an inductor in series in a similar way to a capacitor in parallel (shunt). So, your 5V line is going through a long cable and may have picked up some noise along the way. A series inductor might help.


Anything more specific/complicated than this will require real knowledge of circuits. Any arbitrary placement of capacitors or inductors is likely EMI/ripple/noise mitigation. 

So, if you're a hobby electronics sort of person, and your 5VDC line is rippling a little bit, trying out a few capacitors to ground is the type of solution you might try. Again, just a very basic example.

edit: There are many, many uses for these components that are used for complicated reasons. The things I stated are an example of the more arbitrary uses of them. Capacitors/inductors in gain stages, op-amp circuits and filter structures are a different beast and are chosen by analysis, not by "experience".