How to remove the old mechanical clock movement
To remove your old movement you must start by removing the weights and pendulum with a cloth as to not stain the brass.
Once you have the weights and pendulum off you need to remove the clock hands. There is a nut on the minute hand, you will need to hold the minute hand with your fingers as you loosen the nut via needle nose pliers, you turn the nut to the left to loosen it. (If your clock has a second hand, this is a press fit just pull towards you.) After you have done this you need to remove the trim around the dial. Usually its just on there with two Phillip screws.
At this point there are two options for getting the movement out of the clock. Either with the moon dial or without it.
With the dial =
Now that you have the weights and pendulum off, and the trim off the front of the dial you can just take the movement out with the dial attached if you want to. If you were to stick your head in the clock case and look straight up and you will see the movement is only in with two screws underneath it. The movement is resting on the seat board and is only installed with these two screws that go straight up and into the movements posts. If you get a long skinny regular screwdriver and take these screws out the entire unit with its dial will come off at the point.
Without the dial =
Next its time to take off the side access panels. The side panels come out usually by means of lifting them up, push the bottom in, the panel will then be able to go down and then out. Now that the side panel is off your clock and you can see in there, and you will see some clips holding the movement to the moon dial (face with the numbers).
As you can see the dial is attache to the movement by four posts that stick out the back of the dial. The posts, the dial, the moon, all comes out by unlocking those posts from the front plate of the movement. Sometimes those 4 dial posts are locked into the front plate by clips that just slide over with your fingers. Sometime there are holes in the ends of the posts with a taper pin holding it secure. A taper pin is a pin that is fat on one side and skinny on the other, just grab the end and yank them out with needle nose pliers. You will need someone in front of the clock while you are on the side of the clock, to catch the moon dial when it falls out of the movement. Some one with gloves as not to stain the nice finish of the clock dial.
Either way, if you read both of the above paragraphs, you have the movement ready to come out of the clock case. The only thing left to check is the chain ends, some times the movement will come right out with the chains and all, and other times the ends of the chains get caught up. To remove the ends of the chains, if you have too, is done like this. The links are only curved back upon itself, and they are not soldered together. So to open the link that the chain end is on, can just be done with two small needle nose pliers and twist it open. Then you can remove the chain end, and the movement will now come right out of the clock case with or without the dial on it.