It will take time, and you need to be extra gentle with them.
My ex had OCD which resulted in him having hands so dry from constant washing that they'd crack and bleed (but he couldn't wear hand cream due to the OCD), one really good tip that worked with him was having him switch to using Aqueous Cream instead of soap when he washed his hands, it works as a cleanser but not as drying. Although if your hands are really dirty then apply this cream before then using soap - the cream will still offer some protection against the soap drying your skin.
Get yourself some O'keeffe's Working Hands Hand Cream, don't use just any lotion as you need something to really help repair the damage done to your hands - also remember lotions with scent etc. could cause irritation too so make your hands even more sore, thus all the more reason to buy a decent heavy-duty hand cream meant for this purpose.
Wear gloves when doing chores, especially things like washing dishes, and wear gloves in cold weather. If up for it you can get gloves you wear on your hands overnight, you apply a thick layer of lotion or petroleum jelly then wear those gloves overnight while you sleep so the lotion doesn't get all over your bedding, the gloves also help to really get the moisturizer into your skin.