An oldie but a goodie, elementary school teachers across the country use this method to teach states and capitals to their students. If you already have a good idea of United States geography, just find a blank map of the country and fill in all the state capitals you already know. You'll need to study whatever you leave off. Spend a few minutes everyday looking at a filled in map, then get another blank one and try to fill it in again. You should eventually find yourself able to fill in the entire map.
Sometimes states have smaller, seemingly insignificant capital cities. It can be tough to remember that, for instance, Albany, not New York City, is the capital of New York, and that Sacramento, not Los Angeles, is the capital of California. Other capitals that might trip you up include Olympia, Washington (commonly confused with Seattle), Carson City, Nevada (commonly confused with Las Vegas), Lansing, Michigan (commonly confused with Detroit), Columbia, South Carolina (commonly confused with Charleston), Harrisburg, Pennsylvania (commonly confused with Philadelphia or Pittsburgh ), Springfield, Illinois (commonly confused with Chicago), Jefferson City, Missouri (commonly confused with St. Louis) and Juneau, Alaska (commonly confused with Anchorage).
Another easy way to remember state capitals that elementary school teachers often use is to sing a song that features the names of all 50 states and their capitals. Singing, like other repetitive actions, helps to reinforce information in your memory. One example of such a song is "Wakko's 50 State Capitols," sung by the titular character in the animated series "Animaniacs." Wakko's catchy little ditty not only gives you the names of the state capitals; it also offers goofy but amusing facts about some of the cities.
Sports teams can help you remember state capitals. Look at a political map of the United States and see if you can think of any professional sports teams based in cities that are also state capitals. Some capital cities, such as Boston, are home to multiple professional teams. You can even try to associate the name of a professional sports team based in a city that is a state capital with the state government. For example, Sacramento is the state of California's capital, and it is also home to the Sacramento Kings. Tell yourself that the "Kings" of California (i.e., the governor and state legislature) live in Sacramento.