Birders can indulge in a wide array of equipment but, most people get by with nothing more than a good pair of binoculars and a field guide. (A good pair of walking shoes are a wise addition to your equipment checklist.)
A good place to start to gather information is the Audubon Guide to Birding. It provides advice on a wide range of topics, with links to other information. Be sure to follow the "What You Need" link.
A good pair of binoculars is probably the most important -- and most expensive -- item that a birder needs. Choosing binoculars can be a challenge, and the Audubon Guide to Binoculars is a good place to start.
Some other useful sources to check for advice on binoculars include:
How to Choose Binoculars (at the Cornell Lab of Ornithology)
Finding the Best Binoculars for Birding (also at Cornell)