Amplify Piezo Sensor
You write,


  The blog post mentions a 0.1uf capacitor in the hand-drawn sketch but the Fritzing diagram shows a 10uf capacitor. I am using the 10uf capacitor.


The Fritzing diagram in the high-sensitivity-vibration-sensor at davidhoulding.blogspot.com shows a 10μf capacitor connected from +5V to ground on the breadboard.  This is a reasonable thing to do, to avoid power supply glitching on that board.  It is ok to add an 0.1 μf capacitor in parallel (that is, in addition to, and connected to the same busses) to the 10μf if you want to suppress some noise as well.

The last diagram in the blog, an “updated circuit diagram showing the refinements for reducing the gain to avoid op-amp output lockup, and DC decoupler on the input”, also shows an 0.1 μf capacitor connected between the piezo node and the first op amp input.  This will block any DC voltage coming out of the piezo from going into the op amp input.  It's likely that any capacitor from 0.05 μf up to 0.5 μf will work just as well there.  A smaller coupling capacitor is suitable for higher frequency inputs, and a larger one for lower frequencies.  The presence or absence of that capacitor probably isn't the problem with your circuit.  Looking at your circuit photo, the wiring looks ok[*].  Perhaps try substituting a different piezo element, or a signal generator if you have one, or a low voltage from a pot varied up and down, to generate a signal into your op amp and comparator stages to see if they are working.  If they aren't working, substitute for the LM358.

[*] Although I can't see if the 220KΩ resistor goes to +5 or to pin 1.  Also is your comparator output connected into digital pin 8 on the Uno?  It looks more like 9 or 10 in the photo.  Also, as a personal preference I'd attach the Arduino end of the ground wire to a pin next to the +5 instead of to the ground next to Aref.