What's required to wire a repurposed cooktop in my shed?
You don't say what region of the world you're in, but that's commonly referred to as a "cooktop" in the US, distinct from an electric range. (which is a standalone appliance that includes the oven.)

But both cooktops and ranges can have "3-wire" hookups in older units, where more modern appliances will now use 4-wire hookups, which adds neutral as the fourth conductor. Two of the three wires are hot, and the third is the ground. With 4-wire hookups, a neutral is also included.

If that is what you have, it requires 240volt (in the US) power. Do you have that in your shed? You would need to hook the two hot leads up to an appropriately sized dual-pole breaker, red to one pole and black to the other, ground to ground.