notice that there are two ends with a pin, or a plastic perpendicular piece sticking out that is closer to one end than to the other.
There are two square ends with pins sticking out of the sides.
Using just your fingers, pull the black plastic hand-setting knob straight off. This is only friction fit, and should not be too difficult to pull off. Please make sure you pull it straight back, and not to one side or the other.
Also, pull the battery door off and remove the battery.
Once you have the battery cover removed, carefully pull the rest of the back off of the clock. You can grasp the cover at the sides - one side in the battery compartment, and on the opposite side - so that you are pulling to separate the back at the TOP of the clock.
Once you have the top of the back piece separated, you should be able to easily slide the back piece up and off of the clock, exposing the movement.
In this picture (below), you can see how the replacement suspension spring fits into place. It is likely that you will see the remains of the broken one in your clock.
Remove the broken piece by lifting the top of the spring (brass ribbon) out of its cradle.
Now it's time to install the new suspension spring. Lay it out so that you can identify the top part properly. As pictured here (below) the top of the spring is on the left. The end on the right side of this picture will hook into the pendulum below.
Turn the clock over so you see the bottom of the clock.
Using the pliers, carefully loosen (but do not completely remove) the two smaller nuts at the sides.
This will allow you to remove the top of the pendulum (carousel) so that you can hook the bottom part of the suspension spring to the top of the pendulum.
The square piece of the suspension spring should fit in the slot of the hook on the pendulum. If it is too difficult to slide it in, you may completely remove the nuts at the bottom and completely separate the clock from its base. This step is optional, but may be easier to maneuver.
See below how the bottom end of the suspension spring hooks into the pendulum.
Thread the top end of the suspension spring through the hole at the top of the carousel.
Hook the top end of the suspension spring to the cradle at the top of the clock (where you removed the broken piece.
IMPORTANT: The plastic pin that sticks out perpendicularly to the brass ribbon on the spring should be TO THE LEFT of the star wheel on the movement.
Now you can either reattach or tighten the base by tightening the nuts on the bottom of the clock.
Make sure the round bottom of the pendulum falls into the large brass piece in the center of the base.
Tighten the nuts at the bottom, but be sure not to tighten them too tightly so that they crack the porcelain.
Before you replace the back piece, test your work. Set up the clock so that the pendulum hangs suspended a few millimeters above the base. Is there enough clearance? Do you need to loosen the center brass piece in the base to allow the pendulum enough room?
Once you replace the battery, you should see the star wheel twitching. Double check that the pin on the suspension spring is TO THE LEFT of that star wheel. As that pin comes in contact with the lever next to the star wheel, the star wheel should come free and push the pin back - turning the pendulum.
Once you see that everything works properly, you can replace the back cover. Be sure to slide it down, into the grooves below first... and then snap it back at the top.
Be sure the pin on the suspension spring is out of your way (pointing towards the clock) as you do this.
Once you replace the battery cover and the dome you should be finished! Congratulations!
A word for the future: You only want to give the pendulum the gentlest of pushes to get it started. These suspension springs break from over-twisting. As long as the pendulum isn't spun a great amount, your suspension spring should last a long time. Your pendulum isn't supposed to spin very fast - just a gentle swing back and forth.
Be sure to reference THIS POST on the proper setup of this fine clock.