Step 1: Cut foam
Building hot wire:
The wire will be best if you can find 1/32" stainless steel cable to cut with. In lew of this, bicycle shift cables are OK, but leave a pattern which needs to be sanded off. Stainless steel wire also works, but it's hard to get it strung on straight. The cable should be mounted to some frame which is very springy, as the cable lengthens a lot when it heats up. The springness lets you set the tension when the wire is cold, and have the same tension when it is hot.
Using hot wire:
Put a voltage over the hot wire cutter which makes it cut smoothly through the foam, leaving little foam fibers behind it. The wire should smoke just slightly once it's cut through the foam. Don't try to force it. It is cutting with heat, so pushing hard will make the wire bend and not speed up the cut. A bent wire means you get the wrong shape. Never hot wire a piece with one person. Get one person on each side of the wire. Mark points on the shape which you want to make sure line up. Number them, so both people are going the same direction around the part. Speed up or slow down to match the other person.
I use spray adhesive to stick the foam to the templates. The propellant in the spray dissolves the foam, so spray lightly from a long distance (1 ft?). Let the propellant evaporate, and then stick the template on.