Shampoo less often. Hair becomes dry when the natural oils produced by your scalp aren't getting the chance to nourish it. Shampooing dry hair every day will make it ever drier and more brittle since you're stripping those oils away on a daily basis. Cut back to shampooing just two to three times a week, to give your hair the chance to receive those nourishing oils.[1]
When you first cut back, you'll notice your scalp producing a lot of oil, since it's used to having to overproduce to make up for how much gets washed out. Give it a week or two and you'll find that things balance out; you'll be able to go several days in between washings without your hair looking dirty.
If your roots start looking a little oily, dry shampoo is a great way to remedy the problem without washing your hair.