How to move a stove from the basement?

You could remove the doors and firebrick, but with the right tools it shouldn't be necessary. Use ratchet straps to strap the stove to an appliance dolly. Once the stove has wheels on it it'll will be easier to move. With two people pulling and two people pushing it should go up the stairs quickly.

 

That is one of the easier stoves to move. I move them all the time by myself.
As begreen suggested, remove door and fire brick first.

A furniture dolly can be used under it, and you lift one end at a time with a 2 X 4 lever. Most Baby Bears are rear vent, so a 2 x 6 fits into exhaust opening and can be used as a long lever to lift it easily while you roll dolly under. The lever can go through the stove from the front as well into flue opening, so it works front or back. Blocking on dolly raises it until legs clear floor.

With steps, I don't keep them on wheels. I lay planks on stairs, 2 X 6, 2X 8, whatever you have. Lay stove on its side at bottom and "walk" up as far as you can. When you feel it may slide back down, attach hand winch with strap around stove. I put a 4 X 4 across door way at top to winch from. Once at the top, get it back on wheels and roll. This works with the largest of stoves as well. Larger stoves and boilers require temporary post under weaker stairs for support.

Same as loading on truck. Ramps, lay on side and winch.

 

This Watts Campbell Corliss steam engine with 10 foot flywheel came out of a basement in Allentown PA.
That flywheel is as heavy as that jewelers vault alone! The pillow block it sets on is another ton and then the cast engine itself.
The connecting rod is about as heavy as a stove. It doesn't take a big guy to move heavy stuff. It's all about taking your time, planning it out and working smart.