Food
Black sunflower seeds will attract by far the most birds to your feeders. It has a high meat to shell ratio; you can watch birds poking though mixes to get to those seeds. In the fall our migrant sparrows and juncos return and they like our wild bird food, so some of that is appropriate in the fall and winter.
Sunflower hearts and chips are enjoyed by all seed eaters and leave no hull mess to clean up. It needs to be kept dry because it clogs feeders when wet.
We’ve thought of having a contest to see how many goldfinches people have seen on a nyjer seed sock (we've seen 10). Those bright little birds are so much fun to watch and are here all year around. The socks are refillable.
 

Want to attract non-seed-eating birds to your garden? Put out suet. Some of the usual suspects will come, but you should see some different birds as well. Suet is a great source of energy especially in the winter.

You can also plant with birds in mind. Berries attract many birds you wouldn’t otherwise see, and red tubular flowers are popular with hummingbirds.

Types of Feeders
If you want to feed the little birds and not all the big ones, your best bet is a tube feeder.  Jays may still get a few seeds from them but they can't 'tank up' as they will on a platform feeder.  Some have a mesh surrounding them to let just small birds in.
Platform and hopper feeders feed most birds, while ground-loving birds like juncos and towhees would prefer you just scatter seed on the ground. 
Squirrel-proof feeders are available in hopper and tube styles.

Water
Often neglected, a source of water is crucial to bird habitat. Often you’ll attract birds you don’t see at your feeder: insect eaters there to have a drink or take a bath.
A birdbath should have gently sloping sides and a sure grip on the bottom. It should be filled with less than 3 inches of water and cleaned regularly. Birds love fresh water- think about putting a water source on a timer so the bath fills 3 or 4 times a day.  Your backyard will become an avian destination!

Placement
The only defense birds have against predators is flight. Placing feeders near trees and shrubs will make it possible for them to feed and escape when they must.  Putting food in a clear space may be good too if there are cats around that hide in shrubbery. 
Set up a variety of feeding spots with different elevations, types of feeders, food and environments. You’ll see a wealth of resident birds and may catch some migrants as they come though.

Hummingbirds
Annas, Allens and Rufous Hummingbirds are resident in summer with Annas here year-round.  Migration is not triggered by food availability, so don't worry that feeding them is going to keep them here when they should be migrating. Hummers need tremendous amounts of energy for their migration so fall feeding is especially important since natural food sources begin to fade.

Buy nectar or make it yourself by heating 4 parts water to 1 part sugar on the stove. Put a little in the feeder and keep unused nectar in the fridge. Red coloring is unnecessary and may even be harmful to birds.

Clean feeders often. A couple tablespoons of uncooked rice sloshed around with water is an effective way to clean one that got away from you (don't put this down your sink...).  A little bit of cooking oil or Tanglefoot Pest Barrier on the feeder hanger is a good way to foil ants. Tanglefoot lasts at least a year but is very sticky so be careful.

The Best-1 feeder really is the best.  The base comes apart for cleaning, it sits flat for easy filling, it is sturdy and even has a gauge on the side that will tell you how many hummingbirds you are feeding.

We know - you're probably just feeding one.  Hummers are very territorial and defend 'their' feeder vigorously.  You'll see others sneak in and get driven off, and, on occasion, wary cooperation. Sometimes there are so many that all bets are off and you have a dozen or more hummers trying to feed at once.  You may go through a quart of nectar in a day and being out among them is like being in a miniature air war.  Fun!