First, you need to find out what you have to deal with. Go to the pests and parasites section, and search the threads. You'll find descriptions and pictures. You might need a magnifying glass, and will definitely need a strong flash light, and perhaps a second set of hands to examine the girls at night. Look under their wings, around their vents, at the back of their necks. You'll want to get a good look by parting the feathers, examining the feather shafts and the skin of these areas for creepy crawlies, nits or eggs. You'll also need to check the perches, walls, nooks and crannies for crawling insects. Red mites live in the coop nooks and crannies and come out to feed on the chickens at night. You might hear the chickens stamping their feet on the perches to try to get away from the irritation caused by them. Lice and several other kinds of mites live on the birds themselves. You may have a combination of problems. There are a number of ways to deal with the problem, and a lot of options for treatment. If you have a big infestation, which it sounds like you do, you'll probably need to treat the birds, as well as thoroughly clean and wash the coop a minimum of 2 x about 7 - 10 days apart. In the heat of the summer, i'd go with the 7 days. There are several topical agents that you can use, similar to the products used on cats and dogs for flea control (a liquid that you put several drops on the back of the birds neck. It kills any insects that suck blood (mites), but not chewing insects(lice).) All of them are off label, meaning they weren't designed to be used on poultry, and you'll have to answer the question for yourself about your comfort level using them, and the withdrawal time before eating your eggs again. There are also powders such as permethrin that can be used on the birds and in the coop, but you need to be careful with these due to the birds delicate respiratory systems. There is no withdrawal time for permethrin.
Having an infestation of bugs does not make you a bad chicken keeper. You are to be commended to notice the problem, and take action to protect your flock. Left untreated, birds will be miserable, their egg production will decrease, and an infestation can kill birds. Do your birds have a place to dust bathe? After you get the problem under control, be sure they always have a dust bath available. You can put sand, peat moss, and wood ash in it to help them eliminate further problems.
Dealing with mites and lice is exhausting. I wish you the best of luck.