How do you know the size of the sprocket?

The most commonly used characteristic is the tooth count.

A vernier caliper would be my choice for measuring the thickness of the sprocket (which has to work with the width of the chain) for which there are several options available depending on bike/drivetrain type.

the 3rd size it can be helpful to know is how the sprocket attaches to the hub. Again several options available. But knowing which kind of drivetrain it is should usually be enough to get you the right part.