I love watching and photographing birds in my backyard. It’s always fun to see a new kind of bird in my yard that I’ve not seen there before. I’ll run for the bird book, wildly flipping through pages until I’m able to identify it. “It’s a spotted towhee!”
There are a number of things you can do to attract birds to your yard. Putting out feeders is one of the best things you can do. Different birds are attracted to different types of bird food, so put out a variety of seeds and suet, as well as a hummingbird feeder, to attract a greater variety of birds. Not all types of birds will eat at a feeder, so make sure you think about the ground feeders as well.

House Sparrow
Another great tactic is to put up a bird bath or some sort of water feature. Watching birds splash around in the water is very entertaining and makes for some great photos.

American Robins at the bird bath
The best time of the day for backyard bird photography, in my experience, is in the morning. Not only is that when the birds seem to be most plentiful, but that’s when your best light occurs. Late afternoon is a good time too. You’ll tend to see a greater variety of birds during the spring migration.
The key to getting great photos of your backyard birds is to get close. However, birds are skittish and will scatter at the first sign of movement. What to do? The best thing to do is have a nice long zoom lens on your camera. If you have a DSLR, a minimum of 200mm, but preferably 300mm or longer, is necessary. If you have a point-and-shoot, the higher the x-factor the better (i.e. 10x optical zoom). Some of those point-and-shoots can zoom in pretty close and get great shots. If you don’t have super zoom capabilities, just make sure you shoot at the highest resolution possible so you can get a good crop.

Black-billed Magpie with lunch
Another trick to getting close is setting up a feeder or bird bath fairly close to a window. As long as the window is reasonably clean and there’s no glare, you can get great shots through a window.
Since birds move quickly, it’s a really good idea to use a tripod if possible and shoot at a fast shutter speed.
My all-time favorite place for backyard bird photography is my dad and step-mom’s yard in the high desert of Globe, Arizona. They get an amazing variety of birds coming through and the quail are especially delightful to watch. Following are a few photos I’ve taken during visits to Globe:

Female Gambel's Quail

House Finch

Curve-billed Thrasher

Cactus Wren

Male Gambel's Quail
The very best advice I have to offer about backyard bird photography is this: Be patient.
For additional information about attracting birds to your backyard, check out the National Audubon Society’s book North American Birdfeeder Handbook (which has great information even if you don’t live in North America).
I also highly recommend getting a good bird identification book appropriate to the area where you live.