Prepare scale drawings detailing the proposed addition to your home. Include on the drawing directional indicators (which way is "north"), as well as property lines and adjacent streets and/or alleys. Include the scale to which the drawing was drawn (for example: 1 inch equals 1 foot). Also prepare a rough estimate of the entire cost of the addition.
Submit the drawings and cost estimates to the department in your municipality that governs planning and building. In cities and larger towns this will most likely be an office of the city government. In smaller towns and rural areas this may be an office of the county government. (Start with the department that issues licenses.)
After you receive approval for the plans, submit proof of approval to the division of the department that governs building permits. You should receive an answer either way within two weeks.