As with good photography of any subject, it begins with researching what you want to photograph. Knowing the behavior of the particular species is important. What it eats, where and when it feeds, its flight pattern, in what direction it will take off, to where it migrates, and what are its agitation signals are all facts you should know. They help increase the chance of obtaining great shots.
With regards to bird portraiture, filling the frame should be a primary goal. This means getting the entire bird in the frame or better yet, getting so close you capture the elusive head shot. To accomplish this with small birds, it's essential you have a powerful telephoto. The drawback is they are very heavy and cost a lot. This is why beginning bird photographers start with larger species that are more tolerant of people. A local duck pond is a good place to find cooperative birds. Subjects allow you to approach them so shorter and slower telephotos still net powerful images. If you're restricted by the equipment you have and don't intend to lay out big bucks for a super telephoto, try out your local zoo. Head to the aviary and watch where the birds perch. Another option is to set up a feeder outside a window to attract local song birds. Hang a cloth with a whole cut into it through which you can place the front element of your longest lens. This will act as a blind. Monitor what time the birds like to feed and fire away.
As with most birds, the males are more colorful than the females. For this reason, the males are sought after as they yield more vividly colored images. Get to learn the differences of the males and females of each species to be able to identify your subjects. One of my favorite times to photograph birds is in the late winter and early spring as their plumage is peak. There are many guide books that help with identification. Most are filled with good information regarding where and when specific species inhabit various regions of the US. iBird photo is a great app that not only provides identification photos, it also has recordings of their songs.
As with any subject, factors that contribute to the success of a great bird portrait are good composition, lighting, and how the background is handled. Depending where the bird perches or decides to stand can make or break the potential portrait. The farther away from the background the bird perches, the more out of focus it will be. Branches or other natural elements can act as major distractions especially if they're across the front or growing out of the subject's head. Wait for the bird to move to a cleaner location or perch on a branch that's free of distractions. Sunrise and sunset are the best times of day to produce your images as the color, direction and quality of light net the best images. Flash can be used to add fill light if the bird is sidelit. In that long lenses are the norm, use a Better Beamer flash extender to throw the light farther. If the skies are overcast, flash with a Better Beamer can be used as a main light.