Befriending crows doesn't appeal to me much. Their dark and ominous ways freak me out a little. My neighborhood murder (which really says all you need to know, doesn't it?) perch in the tree outside my front door for hours at a time, squawking loudly, presumably at my indoor tabby cat who's imprisoned behind the front window.
However, if YOU want to make friends with crows, be my guest.
Find some food that the crow seems to like. This requires some trial and error, as they can —or maybe it's just the urban ones who can—be surprisingly finicky. You'll know the crow likes it judging by how quickly it swoops down to grab it. If that pile of leftovers sits all day, they just aren't interested, so try something else, only make sure it's healthy. Crows like junk food, but giving it to them is probably not a kind thing to do..
Stock that food. Buy enough so you don't run out. I buy huge bags of unsalted peanuts from Costco...
Establish a regular feeding schedule, so they know when to expect you and vice versa. If you don't establish a rhythm for interaction, the relationship may never gel. And don't feed them so much that they become dependent—just a handful of something to show you care.
Be dependable, steadfast, and observant. Don't just throw the food out there and walk away. Stay (at a safe distance) to watch them eat (or select carefully and fly off to cache it for later). Since crows have territories, take some time to try to get to know how big your local crow family is...
Don't try to get too close. These are wild animals, after all. Your goal shouldn't be to tame them or take them as pets, which is illegal in most states anyway, and ethically dubious. Even after years of friendship, a crow will be skittish and standoffish (but admiring from afar) and it's better this way.
You know they can recognize people's faces, don't you? Godspeed, bird lovers, godspeed.