Patience is Key
Birds are skiddish and have great eye sight. Wandering around looking for birds of prey is the wrong approach. This isn't landscape photography, The right approach is to scout locations beforehand, then arrive early and wait for the birds to arrive or fly. Getting a successful photo is dependent on stealth and blending into the environment.
Direction of flight
Large birds of prey like to take off into the wind for more uplift so it’s best to stand downwind. This means if you position yourself accordingly, you’ll get the birds flying towards you for a better shot, with a better view of their heads, eyes and wingspan.
Speed it up
You’ll need to use a fast shutter speed to capture birds of prey as they move quickly. Some will tell you that you should use aperture priority with a wide aperture, somewhere around f/4 or f/5.6 on a telephoto lens. They will tell you this so you can use a shutter speed of at least 1/500 sec – or, better still, 1/1000-1/2000 sec.
Keep your distance
Always be aware of what’s behind your birds. Move around so the background is clean and uncluttered. Make sure you compose your shots so the background is as far away as possible – it’s better if it’s 50 feet away rather than 10 feet away, as the further away the background, the more it will be blurred out of focus. The background will be less distracting and your subject will stand out more.
A 300mm telephoto lens on a camera offers a great focal length for shooting wildlife as it blurs backgrounds well. It is also much more affordable. However, using a 500mm lens or 600mm lens will get you that much closer to your subjects for more intimate results, plus it will totally blur backgrounds into insignificance!
I shoot in full manual mode when I am photographing birds of prey. My aperture is usually between f8 and f11 to help ensure i capture the whole raptor in focus, and my shutter speeds are around 1/1200th of a second. The variable setting, depending on ambient lighting, is my ISO... my ISO ranges anywhere from 400 to 1600... my philosophy is I would rather get a photo in focus and fix any noise issues in post editing rather that getting a blurry image because i had a smaller aperture and slower shutter speeds.
I hope that helps...