Begin by melting a small amount of solder on the iron, then push the tip of the magnet wire a small distance into the molten solder and hold it there for a few moments. The enamel will bubble away and the solder will tin the copper underneath in the process. The trick is to use fresh solder, and to clean the tip in between applications. You can see him demonstrate this around the 1:00 mark in the video embedded below.
Once the tip of the magnet wire is tinned, it can be soldered as needed. Magnet wire bends well and holds its shape nicely, so routing it and cutting to size isn’t too difficult. [Tom] also suggests a good hands-free PCB holder, and points out that 0603 sized SMT resistors fit nicely between a perfboard’s 0.1pads.