Step 6: attach wires to LED leads
Solder the wire linkages to the trimmed LED leads on the buttons. For each joint, hold the twisted end with the solder blob next to the LED lead, pressing down to make the wires parallel to the surface of the button. Hold with tweezers, if necessary. Heat it until the solder flows, and then remove the soldering iron tip and hold the wire junction still while the solder cools.
If the wire has been prepared with a big enough solder blob, then you will not need to add solder in this step, making it easy to do with two hands.
The button should act as a heat barrier, and protect the fabric while you are soldering. Use caution to not drip hot solder on the faux fur (acrylic melts!).
Note that the wires are oriented so that the insulated wire adjacent to the solder joint is supported by the button, rather than hanging off the edge where it will be vulnerable to damage.
Join all the (+) leads with one chain of wires, and join all the (-) leads with a second chain. Trim sharp points as needed.