how can i take apart my clock face?

If the hour hand is loose then just push it toward the face at its base. The hour shaft is tapered so that when you push down on the hand base it becomes tighter. To take the movement off you first have to take the hands off. The minute hand will probably have a small nut holding it on. Remove the nut, minute hand and pull on the hour hand. After that the movement can be separated from the face.

Stevens Clocks
February 2013

Have you considered approaching it from the other direction - removing the glass to get to the hands?

Peccavi
February 2013