Start by cutting the bottoms into quarters with a machete. Continue cutting the bottom into 16 slices. This process is easier with a tin snips. You can find a decent tin snips in most feraterias for 5 - 8 dollars.
One at a time bend out the slices and cut them off about an inch from the edge to make tabs. On a KLIM can the first of the concentric rings pressed into the bottom is a good guide.
To connect the cans hold one on top of the other and bend the 16 tabs of the top can around the lip of the bottom can. Start by bending tabs on opposite sides to keep the cans from coming out of alignment. It is easier to avoid cuts if you reach down through the top instead of up through sharp edges of the bottom.
The chimney can be attached to the existing stove using a 3:1 mixture of powered clay to cement. Dig an inch or two into the surface stove to give the chimney an indentation to sit in. Pack the cement mixture in around the bottom end of the chimney. Secure the upper part of the chimney to the structure above the estufa. This will keep the chimney from being knocked out of place.
Over time heat makes the cans brittle, but families should have plenty of time to collect enough cans for a new chimney well before the necessity arises.