How to make a Piezo Pickup

Materials:

Copper foil shielding, eg. 3M 1181 EMI Copper Foil Shielding Tape with conductive adhesive
Shielded hookup lead, lightweight & high quality eg. Mogami
Jack socket, eg. Cliff
Velcro cable wrap

Method:

Solder to jack and piezo film (piezo will de-laminate if heated, so I recommend holding it in a clamp while soldering as quickly as possible).
The bottom layer of the piezo is not covered by plastic insulation so you need to connect its terminal to the negative/shield wire:

Insulate the positive wires at both ends with tape; leave the negative/earth uncovered:

Completely encapsulate the pickup and jack with copper foil, making sure it contacts the negative/shield wire and does not touch the positive:

Heatshrink on the jack makes it look tidier (I tried heatshrink on a piezo but the heat destroys it); a little cork gasket material (or slice of wine cork) on the under-side or the pickup helps make more consistent contact between bridge and piezo:

Notes:

On a Double Bass or Upright Electric Bass they an be attached anywhere on the bridge, but by far the most successful method is under the bridge foot. You can use one or a pair - I didn't find much difference in performance. They work well under the bridge of other stringed instruments.
The MSI piezo films are the same ones used in commercial pickups selling for hundreds of dollars. The sound from the pickups I've made is as good as any of the commercial ones I've tried.
Piezos will create lots of hum if there's a gap in the shield. These ones with full copper foil encapsulation are dead quiet.
Piezos have a very high impedance so it is usually recommended that they are plugged into a buffering preamp with input impedance of 1 Meg Ohm or higher. However if you mount them under the bridge they have high output and you may find they sound just as good plugged directly into an amp or DI. If not using a preamp. keep the connecting lead as short as possible.
The Velcro tab lets you fasten the jack to the strings behind the bridge, which has the added benefit of damping the strings against resonance or feedback at high volume:

David Fittell 2005