Step 3: Sometimes things get dirty and dry
I typically clean these old movements by first removing the movement from the housing, shooting some WD-40 around all moving parts (to blast away grit and solidified oil), then lightly oiling it with a very fine machine oil (such as sewing machine oil). In most cases this will get these old wind-up clocks running again.
Occasionally a mainspring will get dirty or develop a light coat of rust. WD-40 tends to fix this as well. Many people believe a clock can be overwound, but there is no such thing. Clocks were made to be wound completely. If it's not running, more often than not it is either a lubrication problem on the balance wheel, or a dirty or rusted mainspring.