I haven't raised any baby crows, but I have looked after baby starlings that fall off my roof every now and then. I keep them in a warm dry place and DON'T give them any water if they aren't fully fledged as they get all the moisture they need from their food at that age and water can risk killing them from drowning, even a teeni drop. If the chick isn't getting enough moisture from the food, then gently wipe some water on the beak, not drip or syringe it in. I fed the starlings brown crickets as I used to have a tarantula, as well as some wild bird seed from the seed mix we feed the adults and some mashed up strawberries and blackberries from the garden, and they loved them, and when old enough to fly, I let them go free.
As for crows, they need to be fed between every 10-20 mins and the water rule applies to them also... Scrambled egg, bugs you find in your garden, low phosphorous cat or dog food, cooked pasta, whole grains, chicken, beef, mashed fruit and berries, peas and green beans, nuts, peppers (bell or chilli), peanut butter and mashed potatoes are all things you can feed them. Make sure the crop is empty between the feedings or else it may suffer a soured or impacted crop. It is important for the chick to have a varied diet if it is to grow healthy and strong.
Also, be careful of anything that can or could be broken and shredded, as the moment the chick is old enough to start fluttering and hopping about, they WILL destroy everything in curiosity.