Two main signs you need to look for
1) take a bit of kitchen roll and run it on the underside of the perches - if you get specks of blood you've got red mites in your hen house. Best to check first thing in the morning because these sods are active at night.
2) check round cracks and crevices - if you see white "dust" that's also a sign.
You have to keep checking because they feed on the girls' blood at night. If you have an infestation and you don't know about it, it can make your girls anaemic and can kill them if left. They are an absolute sod to get rid of, but a double dosing of Poultry Shield (I do it once a week when I've seen evidence of the blighters) and then putting diatomateous earth in the bottom of the coop, in their dust baths and on their perches seems to deal with it. I also treat the girls with Mite and lice powder (that's a two man job - one to hold the girl and spread her wings, one to shake powder everywhere).
It is quite satisfying when you spray your hen house with PS and then after half an hour there is green gunk running down it. Then you know you are killing the little buggers.