We have hummingbirds in our neighborhood year-round. There's one feeder hanging outside our master bathroom window, and another hanging in our back patio. They are constantly buzzing and chirping.
I use a tripod-mounted Nikon 300mm f/4 lens most of the time when photographing hummingbirds, although I have hand-held it on some occasions. Mounted on a Nikon DX DSLR, like my D300, the 300mm has an angle of view equivalent to a 450mm lens mounted on a 35mm film or full-frame DSLR. I can never get close enough to get some really cool shots taken by my friends that I've seen.
Usually the best light for me has been during the late-afternoon or early evening like this:
In the mid-summer's early evening the birds are backlit, which outlines them nicely but can pose an exposure problem:
In the former picture I did not add any exposure compensation, but in the latter picture I added one stop. I just took a picture, previewed it and looked at its histogram, then adjusted my exposure accordingly.
I've always liked this hummingbird picture best:
The light was wonderful in how it sculpted the shape of the bird and also how there is detail in the shadows and yet the highlights aren't overexposed.
Finally, I only have two flying hummingbird pictures that are worth sharing, so I picked this one:
I used shutter-priority on all these pictures because these birds are fast; just pick a fast shutter speed (like 1/1000 second or faster) and let the camera worry about picking the aperture.
(Shot with the Nikon D200 using a Nikon 300mm f/4 lens; shutter-priority with shutter speed set between 1/800 second and 1/1250 second; normal or fine JPG.)