Let's begin with my camera setup. I always walk around with my camera set to Manual with a shutter speed of 1/2000 and a aperture of F/5.6. I have the camera set to Auto ISO (letting the camera choose the ISO needed). I use autofocus mode AF-A, with Nikon cameras this mode uses Single Focus when a subject is stationary and switches to Continuous Focus when a subject is moving. Is it perfect... NO, but it is almost perfect. I always have these settings on the camera because I can quickly pick up a bird in flight where as for perched bird I have time to quickly change the shutter speed.
For exposure I always use Nikon's Matrix Metering, it evaluates the whole scene in the viewfinder and computes an exposure. Now here is where it gets tricky. In most instances because the bird is not filling the viewfinder/image the camera is going to be biased to exposing for the background (Sky or vegatation). So you have to tell the camera how to expose the image. I use and have my index finger on the +/- EV button and my thumb on the wheel controlling the settings. Clockwise is adding exposure and counter clockwise is subtracting exposure.
For bright backgrounds and birds brighter than the background (white) you need to underexpose or the camera will clip the whites on the bird. It varies from -1/3 to as much as -2 depending on how bright the sun is. Here is a Great Egret I captured at -1 EV.
For bright backgrounds and dark birds (brown, black etc.) you need to overexpose to keep the shadows on the bird from blocking and the bird becoming a dark blob full of noise. Most times it is between +1 to +2 depending on the light. Here is a Double Crested Cormorant that was captured at +1 EV.
For bright backgrounds and mid-tone birds most times the camera can do a good job without any corrections. Here is a Great Blue Heron captured without and correction to the camera exposure.
This next image is a special case. If it had not been overcast I could have captured it without correction, the background was mid-tone and the bird was basically mid-tone (light brown). The image as shown was captured at +1 EV to make up for the dark overcast and to reduce noise (exposed to the right). The ISO for this image was 3200 (Christina take note). It is a Limpkin gliding over the marsh.
Find out what works best and change exposure to suite the conditions.