Instructions
Buy a field guide. Often, all you see is a silhouette from the ground, and field guides give you these. You can also purchase software that is essentially a database. You enter information about what you observed, and the software will narrow down the search for you. Then you can view a short video of these raptors in flight, along with their call, from the list.
Buy a good pair of binoculars specifically made for bird watching or nature. These binoculars tend to be lighter in weight (you could be waiting a while), have clearer vision for dusk and dawn lighting, and give you the magnification you need. Practice using them to follow birds in flight.
Look at the bird's flight habit, as well as the shape of its body, wings and tail. For example, a turkey vulture can be a dead give away because it flies with its wings forming a V pattern and its tiny head is almost invisible. By contrast, a red-tailed hawk extends its wings outward even with its body, and the head is large enough to see from the ground.
Listen for the call of the bird. If you're lucky enough to hear it, this information alone may be enough to identify raptors in flight. It will definitely help narrow down the possibilities.
Refer to your field guide or video to piece together the information you have after observing and listening to the raptor.