chain-link pliers being custom-designed for the job, I'm sure they work really well. But I get by with the lift-and-bash method. I can't find the illustration right now, but you put the chain on the big ring with the masterlink at 3:00, work one link of slack into the chain so the masterlink and its neighbor are poking up off the chainring like an A, then use a hammer (or a rock) to tap whichever plate of the masterlink needs to be tapped to open it up.

But you will need a chain tool to push a pin out of the old chain to get it off (or maybe try a dremel with a cutoff wheel?), and to shorten the new chain to the matching length.