Some very good advice here. I spent a lot of years trying to outsmart the 'black devil bird'.
7 1/2 shot works well up close, but 6 really knocks them down on the longer shots where 7 1/2 will only break the near side wing.
Camo everything, face, hands, and gun. Do not let them see you move at all, even the tiniest movement will give you away. Wait until they are so close you can see their black beady eyes. If they are flying directly over you they generally do not seem to see (or look) straight down, mostly they seem to look down and ahead. If they get almost directly overhead they will be looking past you, then you can swing on them and they won't catch the motion. This will give you a going-away shot where you can see the bird over the bead, rather than having to lose sight of an approaching bird behind the muzzle as you swing through to lead it. They can turn or even just about stop so fast that on such a shot they can swerve and you won't see it before you shoot.
They may come in singles, doubles, or flocks. If you have been observing them for a while you will know what to expect. If you know there is a flock in the area, they will send a lone sentry to investigate your calls. DON'T shoot it! Let him go back with the all-clear and then the flock will come in. Otherwise you'll get just the one bird and that's it. They can sneak in from any direction at any time, so beware.
They have three levels of security: a few sentries that sit quietly in treetops and observe everything, low silent drifters that ghost along at treetop height, and SR-71 blackbirds that fly so high they must be on oxygen. A large flock will deploy all three levels and any one can bust you and warn off the flock. So, it pays to know the habits of the area you hunt. A flock will roost in a particular place, and have flying paths and patterns to food and water and back. Learn these and set up somewhat off to one side of their prevailing paths and pull them in. Don't hunt the roost or major food areas, you will cause them to move or change their patterns.
Dead crows and/or a crow distress sound can drive them into a frenzy where they will completely disregard you standing in the open and firing as fast as you can. A distress call can even bring one back to you that you just missed. When you get a couple of dead ones, put them out in plain view, play a crow fight, then a crow distress. If some come in they may throw caution to the winds and go nuts, dive-bombing the corpses. They won't even notice you. Not a common event, but I've seen all the above, and it's something to try to use against them.
Learn to use a mouth call and learn to 'talk crow'. They do have a specific language (I used to know it pretty well but now forget). A quick blast of a distress call from a mouth call in the middle of some wild action can turn the tables in your favor. I recommend the Olt E-1 call, it's very versatile in terms of the different sounds you can make with it.
Oh man, did we have fun back in the 'good old days' of crow hunting when I lived back east. Took me years to get over the withdrawal symptoms (twitch twitch).