There's no breadboard (or PCB) required as the wires go directly between the PSU, LED strip and Arduino. But the Arudino has those connectors that I used as opposed to soldering on the other side of the Arudino. The cables run onto the connectors that came with the strip (bare wires soldered together and covered with electrical tape) and also from the strip to the PSU.
Attached photos of all the connections.
Arduino:
PSU:
LED strip connectors, wire to wire connection and LED strip in the background:
