Contact city hall and ask which department is charged with keeping such records; usually the city permit, records or zoning department. Provide the proper agency with the address of the structure in question and ask what forms or information are required for you to obtain the original floor plans. Permitplace.com has a listing of agencies responsible for such recordkeeping in various cities.
Connect with the architect who designed the building. If the city doesn't have records of the floor plan, try to reach the original architect to see if he has copies on file. Architects usually keep copies of all their work.
Contact the builder to see if she has a record of the floor plan. Most large building contractors will keep records of the buildings they've worked on.
Ask local real estate agents. Realtors familiar with buildings in the area can often direct you to the right source for building plan information.