Instructions
Consider the overall shape of the clock first of all. The chalet style -- in which the clock looks like a little house with a steeply pitched roof -- was introduced in the 1850s. If your clock has a more boxlike appearance, then it might date to before that time.
Look next at the pendulum. Late 19th and 20th century clocks often have multiple long pendulums swinging beneath them; on earlier examples, the pendulum was short and suspended in front of the dial.
Open up the back of the clock and look at the movement. Clockmakers made the mechanical parts of the earliest cuckoo clocks almost entirely of wood. Over the 19th century, brass replaced more and more of the pieces. By the 20th century, most clocks were fitted with cheap, mass-produced metal movements, and from the 1950s onwards, manufacturers also made electrical cuckoo clocks. Because the change from wood to metal parts occurred gradually, looking at the mechanism is perhaps the best way to judge a cuckoo clock's age.
Listen to the cuckoo's mechanical "song." If its notes are strong and lusty, then the clock is probably of 20th century vintage. A frailer sound suggests that the miniature bellows that power the cukoo's song are starting to perish, which points to an earlier date of manufacture.