I hear plywood's good enough, so I'll follow what I was told and make it out of plywood.
Literal
Plywood [with-で] enough [copula-だ] [quot-と] thing, taught way plywood [with-で] make [thing-こと] [decide-にします].
~とのこと is the hearsay report frame: 'I hear that X / it's reported that X' — softer and more formal than って or ~そうだ. ~通り 'just as / in the manner of' — here 教えられたとおり 'just as I was taught.' ~ことにする 'to decide to X' marks a personal resolution or choice ('I'll make it my thing to X'). The instrumental で appears twice, both times marking material: 'with plywood.'