The foundational way to use Clocks is as a representation of either (a) "You Complete X" or (b) "This Thing Happens". As I learned of them through
BitD my go to example would be as a heist. So you've got a Clock A, which is the players making progress toward their goal, and Clock B, which is whether the alarm for the guards is raised. In 5e terms, you would present obstacles, ask for skill checks, and whether or not the PCs succeed on the roll or not (and you can choose to use degrees of success/failure rather than a strict binary) determines how much of each/either clock you fill in.
The physical representation of the clock itself is like a Pie Chart. You're filling in wedges for each success/failure
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Another way to incorporate these into 5e would be through downtime activities. If your PCs have downtime between adventures, you can have them roll to make progress on projects they might be working on, like researching or a spell or a demon lord's truename or crafting a magic weapon or gathering ingredients for an extremely powerful ritual.