And how do you tell if it's an active den?

lightly dust the entrance with a thin layer of flour in the evening. check the tracks in the morning

Remember though that the den may have other animals other than fox or coyote such as skunks or snakes so use caution. If you are unable to see the tracks you can also put crumpled paper in front of the den. If the paper is moved and you have not had a heavy wind storm you will know at least something lives there.

Why do you want coyotes around?

Coyotes keep the rodent, rabbit and even baby deer population in check. Plus, they are part of a healthy, diverse natural network.