Scissors and shears are the primary cutting tools in puppet building, and the single most important rule about them is that you need more than one pair and they must never be used on each other’s materials.
Fabric shears
are long-bladed, bent-handled, and sharpened to slice woven and knit fabric cleanly. They cut fleece beautifully. They are ruined permanently the first time somebody cuts paper, card or foam with them, because those materials dull an edge in a way fabric never does. This is why builders label them, hide them, and get genuinely irritated about it.
Foam scissors
are a separate pair, and they take punishment. Foam is abrasive and blunts blades fast. Serrated or micro-serrated blades work noticeably better than smooth ones, because the teeth bite the foam rather than compressing it ahead of the cut — compressed foam springs back and gives you a wavy edge.
Small sharp snips
for detail: trimming felt at a mouth plate edge, notching a curve, clipping thread. A large pair cannot do fine work no matter how sharp.
Cutting fleece specifically
Long confident strokes, not short chops. Fleece is a knit and it stretches under the blade, so short repeated cuts produce a scalloped edge. Let the weight of the shears do the work and cut in as few passes as you can.
Cutting fur
Cut from the back, through the backing only, with the blade tips — never straight through the pile. Cutting through fur from the front hacks the fibres and leaves a visible bald seam that will not brush out.
The hack: tie a coloured ribbon on your fabric shears. It is a stupid trick and it works.