How do I make a good electrical connection with wire I can't solder?
Figure 1. An insulation displacement connector (IDC) box.

Wires are pushed down into the terminals using an expensive professional push-down tool with built-in cutter or a cheap plastic pusher. The blades in the IDC connector displace the insulation (by cutting through it) to contact the wires.

 

Figure 2 and 3. The "pro" tool and the cheap plastic pusher.