I suggest you go straight to your state's website and do a search there. You would be surprised how often these documents are requested. Often information about replacing documents is in the FAQ or very easy to find.
The Center for Disease Control and Prevention has a page on which there are links provided for where one should write for vital records in each state. Links for all fifty states, the District of Columbia, American Samoa, Canal Zone, foreign or high seas, Guam, Northern Mariana Islands, Puerto Rico, and Virgin Islands are provided.
The methods for obtaining a birth certificate may vary by state, but in general there are different prices for doing it in person, by mail, and over the internet.
You will most probably be asked to provide the following information: name at birth, birth date, city and county of birth, gender at birth, parents' names including mother's maiden name, your relationship to the person named on the birth record, a valid reason for the request, and your signature, daytime phone number, and mailing address. All of this, of course, may vary slightly by state.
You will have to pay something. Mine cost a total of $35 with processing fees and shipping. If you can go to a state office in person to get one that may be the cheapest and fastest way.