There are only two real requirements needed to establish a United States Golf Association (USGA) handicap, making it something just about every golfer should have. You must belong to a golf club, the definition of which established by the USGA is fairly open and includes many public facilities. And you must have at least five scores to calculate your handicap. A few other details might interest you.
Establishing a USGA Handicap Index
Private clubs: Most private clubs are listed with the USGA as member clubs and provide handicaps as a service and condition of membership. Your handicap fees are factored into your membership, and you can post all of your scores for the year and play against other golfers of differing abilities using your handicaps to adjust games to a more level playing field.
Public: Many public golf courses around the country host golf clubs–some with open membership–that offer handicap service. Fees and dues vary by club. Public courses can also be USGA member clubs and provide handicap service for a fee. Inquire with management where you play golf about how their handicap or club system works.
Post scores: Once you've established a USGA handicap, you should post all off your scores through the year. This is how the handicap system maintains its equanimity. As long as you post all your scores, your handicap accurately reflects the type of golfer you are. You must have at least five scores to establish a handicap, but the full algorithm bases your index on the best 10 of your last 20 scores.
Online posting: The USGA maintains a website under its Golf Handicap and Information Network (GHIN) where players can post their scores virtually regardless of where they've played anywhere in the country. Not every club allows its members to post online, but more and more are taking advantage of this service.
Your card: New handicap cards are issued by the USGA to every member club every two weeks during the handicap season. Make sure you have your most up-to-date card with you when you play to avoid any disagreements with your playing partners.