Using a chain tool

Tighten the chain tool onto the chain pin. Be sure it is lined up exactly.

Begin to remove the pin. You will notice three phases of resistence as the pin comes out:
--First, it will be very tight as the pin clears the sideplate closest to you
--Second, the pin will move easily, while the chain tool is pushing through the middle
--Last, the pin will begin to give more resistance. STOP. DO NOT let the pin come all the way out. Leave it sticking out of the end of the sideplate. Try to remove the chain by lightly trying to "break" it as one would break a small twig. If that doesn't work, re-insert the chain tool and remove one more milimeter of pin.

To put back together, just line up the chain again inside the chain tool, and push the pin back into the chain. When its back in, it will be very stiff, which is solved by lube, but mostly by lateral pressure (the twig breaking motion, but harder.)