It is not necessary to remove the back plate to replace the Delta Monitor cartridge. It is removed in the images because this faucet was just installed. If you have this type of handle you will need a very small Allen key wrench to remove the set screw that is in the base of the handle, just look for the little hole in  the handle.

This image is of a Moen Positemp shower faucet but the location of the set screw is in the same place as the Delta Monitor. Remember you can click on the image to see a larger image. If you have the plastic ball handle remove the button with the Delta logo on it then remove the screw.

Once the handle is removed you will need to remove the chrome sleeve, just grab it and pull it straight out towards you. it does not need to be turned, but turning may help it come out. Again the back plate does not need to be removed.

With the sleeve removed the nut will be exposed. this nut needs to be removed. be careful not to put too much pressure on the nut, if you are using channel locks you can squeeze too hard and end up pinching the nut causing it not to turn. hold the channel locks on the very end of the nut (closer to you) to avoid crushing the nut. The nut turns counter clockwise as you face it.

With the nut removed, you can pull the old cartridge out. just grab it and pull straight out. if it is tight try using a small screwdriver between the cartridge and the brass body, being careful not to damage the brass body.

Once you have it removed this far it should just come out. You may want to save some money be trying to repair the cartridge, but you will find that it is just a waste of time, get a new cartridge.

With the cartridge removed this is what the inside of the body looks like, this one has a fitting I have not seen in earlier models of the Delta Monitor tub and shower faucets

It's a little strainer or screen. if your have lost pressure in both your tub and shower heat, this may be the cause. I'm sure Delta has a good reason for adding this screen, but I can not see it. I think it is easer to remove the shower head to remove sediment then it would be to clean out this screen.

I recommended removing this potential call back to the home owner, he agreed and tossed the screen away.

If you click on this image to see the larger image you will notice 3 holes. Bottom left is your hot water inlet, bottom right is your cold water outlet top middle is where the water goes out to the tub or shower. Now you are ready to install the new cartridge.

The cartridge just slides in but you have to line it up correctly note the little V shaped indentation on the brass body and the V shaped nub on the cartridge the cartridge must go in all the way and be flush. to be sure the top is the top note the raised part of the scald guard adjustment fitting is on the right side of the cartridge.

Once the cartridge is installed and flush with the brass base put the nut back on. tighten the nut as tight as you can by hand, you do not need to use a wrench to tighten the nut. With the nut in place you can slide the sleeve back into place If you have the chrome or equal handle make sure the with plastic insert is inside the sleeve

Otherwise you will have a gap like this. now you are done with the replacement of the cartridge. but don't put the handle back on yet. use the handle to turn the faucet off, then turn the water to the house back on. make sure to turn both the hot and cold back on if you turned them both off. You may need to adjust the scald guard feature of the new faucet. with the handle on temporarily turn the faucet on as far to the hot side as it will go.

 Wait a reasonable amount of time to allow for the hot water to arrive at the faucet at max temperature. Test to see if the water is too hot or not hot enough. (keep in mind you can adjust the faucet to a point where someone can be scalded) You take full responsibility for the setting you use. Take a close look at the image above. click on it to see a larger image. Note that the inner ring can be pulled out. 

It does not come all the way out but it comes out enough for you to turn it Notice that it has gears on it turn counter clockwise a few gears for hotter water and clock wise for cooler water. keep testing till you have the hottest water you want then you are done replace the handle.

Important note. The water temperature coming out of the faucet will not exceed the maximum temperature of your water heater. If you raise the temperature of the water heater you will need to re adjust the scald guard feature on the Delta Monitor Faucet.