Solder the JST Connector to Trinket
There is a great demonstration of how to do this here. Notice they are using the Audio FX Sound Board here, but it's the same technique that we'll use on the Trinket. Start by soldering one of the short side pad footprints on the Trinket and tack the JST into place Then you can properly solder the last three pads without it moving around.
Solder a Wire to the PIR Sensor
Usually the sensor is used with a larger battery pack, but in order to use the LiPoly, which is a smaller voltage, you'll need to solder a wire to bypass the regulator. The regulator is labeled 7133-1 and has three pins on one side, with a tab on the other. You will be soldering a short wire from the first pin of the regulator to the pad of the resistor located right near the red wire of the sensor's power cable. Make sure you tin both sides of the wire first, and it helps if you use a third arm and tweezers. Solder the regulator pin wire first, to make your life easier. When finished, plug the sensor wires into their jack on the sensor.