Turn the screw on the chain tool to start pushing the pin out of the chain (see photo). be careful to keep the pin on the chain tool lined up with the pin on the chain, sometimes they like to slip around a bit.
Don't push the pin all the way out! Only push it just far enough so the chain comes apart (see photo). You need to leave the last bit of the pin in the chain so you can push it back in later.
If you want to do this without a chain tool: drill a hole in a piece of wood and place the pin you want to remove over the hole. find a machine screw about the size of the chain pin and use it as a peg to bang the chain pin out with a hammer. It's tricky because you don't want to bang it out all the way.