In order for a amateur-built or light-sport airworthiness certificate to be issued for your airplane, it must be inspected by a representative of the FAA. This can be either an FAA employee or a private individual who has been designated by the FAA to perform these inspections. This designee is called a Designated Airworthiness Representative (DAR).
Due to FAA office budget and manpower restrictions, you’ll find it more expedient to work with a DAR. Not all DARs are authorized to do all types of airworthiness certificates, so you will need a certification inspection done by a DAR who is authorized to issue the particular type of certificate you desire. Use the following link to find a DAR who can issue the type of airworthiness certificate you seek:
The FAA DAR Directory (PDF) provides a list of DARs, by state and technical discipline.