You light it and put the pot on one of the rings.
Seriously, it may look different but it really isn't. You have a heat source, an oven, and a bunch of rings. The only real change would be when you go from a wood-burning stove to a gas or electric one, you don't have to worry about minding the fire.
By the way, did you mention at one point that you were planning on adding more events into the early game? I seem to remember that. In the same vein of discussion, I recall that one of the first things I thought when I started playing the game is that in MC's place, I would try to teach Lin to cook rather than just expecting her to figure it out by trial and error; that could be an event or two of bonding between Lin and MC, before things get sexual.