What is a decoupling capacitor and how do I know if I need one?
Power supplies are slow...they take roughly 10 us to respond (i.e. bandwidth up to 100 kHz). So when your big, bad, multi-MHz microcontroller switches a bunch of outputs from high to low, it will draw from the power supply, causing the voltage to start drooping until it realizes (10 us later!) that it needs to do something to correct the drooping voltage.
To compensate for slow power supplies, we use decoupling capacitors. Decoupling capacitors add fast "charge storage" near the IC. So when your micro switches the outputs, instead of drawing charge from the power supply, it will first draw from the capacitors. This will buy the power supply some time to adjust to the changing demands.
The "speed" of capacitors varies. Basically, smaller capacitors are faster; inductance tends to be the limiting factor, which is why everyone recommends putting the caps as close as possible to VCC/GND with the shortest, widest leads that are practical. So pick the largest capacitance in the smallest package, and they will provide the most charge as fast as possible.
I was the one that asked that question. Here is my rudimentary understanding:
You attach capacitors across \$V_{CC}\$/GND to try to keep the voltage more constant. Under a DC circuit, a capacitor acts as an open circuit so there is no problem with shorting there. As your device is powered up (\$V_{CC}\$=5V), the capacitor is charged to capacity and waits until there is a change in the voltage between \$V_{CC}\$ and GND (\$V_{CC}\$=4.5V). At this point, the capacitor will discharge to try to bring the voltage back to the level of charge inside the capacitor (5V). This is called "smoothing" (or at least that is what I call it) because the change in voltage will be less pronounced.
Ultimately, the voltage will not ever return to 5V through a capacitor, rather the capacitor will discharge until the charge inside it is equal to the supply voltage (to an equilibrium). A similar mechanism is responsible for smoothing if \$V_{CC}\$ increases too far beyond its average (\$V_{CC}\$=5.5V perhaps).
As for why you need them, they are very important in high-speed digital and analog circuits. I can't imagine you would need one for an SN74195, but it can't hurt!
Normally called a "bypass cap", because the high-frequency noise bypasses the IC and flows directly to ground, or a "decoupling cap", because it prevents the current draw of one IC from coupling into another IC's power supply.
"how do I know if a specific chip is one?"
Just assume they all do. :) If a chip is drawing current intermittently, it will cause the supply voltage to droop intermittently. If another chip is "downstream", it will see that noise on its power pins. If it's bad enough, it can cause errors or noise or whatever. So generally we put bypass caps on everything, "upstream" from the IC. (Yes, the orientation of the traces and the locations of the components matters, since copper is not a perfect conductor.)