Remove a shower drain using a drain key or smart dumbbell. Using tools other than those the manufacturer specifically designs to remove the flange is more likely to cause damage to the shower floor or the tool you are using.
Most showers have a screen that is level with the shower floor. Remove the one or more screws that hold it in place, and lift it out of the drain. Insert the tool into the drain for removal. The end of the drain key has a recessed cross that matches the crosspieces you can see inside the flange. If using the dumbbell, insert the largest end that fits into the drain, and tighten the shoes against the drain sides. Turn either tool counter clockwise, and unscrew the flange.
If you are using the proper tool but find removing the drain is difficult, try heating the surface with a blow dryer. The gentle heat does not damage the shower floor, but warming the plumber's putty around the flange makes in more flexible and the drain easier to remove.
Once you successfully remove the old drain, clean the area on the shower floor, ensuring you remove all of the old plumber's putty before installing a new unit. The area around the opening should be dry before attempting to install a new drain.