Prepare the Room
This is going to be dusty, and just generally nasty. Close the doors to the rest of the house, open the windows, remove everything that is removable from the room and cover everything that isn't removable in heavy canvas tarps. (Plastic isn't good enough, as it won't protect items from falling pieces of hard tile.) If there are light fixtures, electric switches or other electrical things on the wall or ceiling you're working on, kill the power to them and take them out. Put on a long-sleeved shirt, tough pants and boots, goggles, a dust mask and very thick hard-leather or canvas gloves.
Find the Seams
The trick to removing wire lath is to loosen it at the seams (where it's connected to the ceiling joists or wall studs). Find the seams by pounding the plaster with your hammer in a straight line running perpendicular against the direction of the studs. As the plaster falls, you'll see the metal screen behind it. As you cross each stud with your hammer line, look for the end of the lath sheet there, which will usually be overlapped on the stud with the next section of lath. When you find a seam, change direction and knock down all the plaster along the seam.
Take It Down
Once you have the seam exposed, use your hammer and flatbar to loosen it all along the stud. It will be connected there by nails or staples that will have to be pulled out. Once it's loose, grab the wire lath with your hammer claw and the hook of the flatbar, and pull downward. Let the weight of the plaster help pull the rest of it down in a solid, flat mass of lath and plaster. The more you can keep it in one piece, the better. Once one whole section is down, work from the edges of the remaining plaster, loosening the lath at the seams and pulling it down.