Many people have great luck, simply hanging out feeders and getting birds to come in to eat. Once you start feeding them, you realize that some birds are more fun to watch than others, so how do you attract those specific birds that you enjoy hearing and seeing? First, research them...find out what they like from trial and error or go to your local library and read a little about them. If you are interested even further, try subscribing to a periodical, like Birds and Blooms, they offer great tips on bird watching from the experts.
If you are planting, try planting some berry producing shrubs and plants in your yard that help attract birds, raspberries, blueberries, elderberries, dogwoods, mulberries, and even strawberries will help bring in birds. I've had great luck with my local nursery and Gurney's online catalog.
Make sure you have a water source, if you don't have a nearby river, creek, pond or lake, put out a bird bath or two. You will notice a large difference in the volume of birds you have arrive. If you don't like what the birds leave behind after they eat, put a windsock, chimes, or other noise device on or near your deck, patio, or childrens' swingset, and place the feeders away from that area.
Try leaving an area of your lawn "natural". I've used different grasses, wildflowers, sorgum, broom corn, and sunflowers to help provide the birds with a natural habitat near my feeding stations.
Some birds, like hummingbirds will come in very close to you to eat. There are many pictures of hummingbirds actually eating out of someone's hand. Others, like Orioles are more easily startled, and will generally not come in close if you are near. So have a variety of feeders in your yard, some that are close to the "people" area and some that are further away, see what different types of birds you attract at each. If squirrels are a bother to your birds, give them their own feeder.
Try your own food. Bluebirds will eat a batch of cornmeal mixed with peanut butter, with some mealworms mixed in for a treat. Experiment and see what different birds enjoy.