Understanding APHIS

The Animal and Plant Health Inspection Service (APHIS) is the agency within the US Department of Agriculture (USDA) with the job of "Protecting America's Agriculture" through regulations, inspections, certifications, and generally overseeing the health of the nation's agriculture, horticulture, and natural resources. Read more: http://www.aphis.usda.gov/about_aphis/
APHIS hierarchy
The Plant Protection and Quarantine (PPQ) program "safeguards agriculture and natural resources from the risks associated with the entry, establishment, or spread of animal and plant pests and noxious weeds to ensure an abundant, high-quality, and varied food supply."  These are the people who create regulations and enforce them; man the Plant Inspection Stations, through which plants and plant parts enter the country; identify and study the pests and diseases which affect agriculture, horticulture, and the natural environment; mount programs to eradicate or prevent such pests and diseases; issue permits to import, and certificates to export, plants and plant products. Read more: http://www.aphis.usda.gov/plant_health/  
Be sure to explore the many options and programs listed in the right-hand sidebar and the Spotlights at the bottom. 
Plant Health Programs
Within APHIS-PPQ, the section for Plant Health Programs is comprised of the individual departments that handle each of the major jobs, including setting policy, writing regulations, settling import/export issues with the U.S.'s trading partners, issuing permits, identifying pests, creating and enforcing import manuals, plus IT support for all of the above. 
Stakeholder registry
If you wish to receive electronic notification of changes/decisions/activity across a wide range of subjects and Acts pertaining to the movement of plants and plant products, sign up for the Stakeholder Registry: https://public.govdelivery.com/accounts/USDAAPHIS/subscriber/new
Information on permits to import regulated plants and plant products is available here: http://www.aphis.usda.gov/plant_health/permits/plantproducts.shtml
The permit application form to use is PPQ 587, which is used for a variety of plant and seed permits.  
Under PPQ 587, click on Plants for planting (including seed). At the bottom of the page, you can click on Apply for a Permit, which leads to this page: http://www.aphis.usda.gov/permits/ppq_epermits.shtml
From here, you can either begin the process of obtaining an ePermit (click on PPQ 587 in the first section), or download a printed form to send by mail (click on PPQ 587 in the second section)
You can learn about the ePermit system, which allows you to do business with APHIS-PPQ online, including applying for or renewing import permits:
Authentication for using ePermits is a two-step process: http://www.aphis.usda.gov/permits/eauth_epermits.shtml
2. Then take the information that you receive from APHIS-PPQ and a photo ID to the 
    nearest Local Registration Authority (LRA), which you can find here: http://offices.sc.egov.usda.gov/locator/app?type=lra
The application requires that you name one or more Plant Inspection Stations through which your imported seeds/plants will pass. The station(s) need not be the one(s) closest to your home.  Choose from the list on this page: http://www.aphis.usda.gov/import_export/plants/plant_imports/plant_inspection_stations.shtml
Further help and explanations are available from:
Customer Support Desk: 301-734-0841; or
Permit Service: 877-770-5990; or
Manuals online
The complete list of APHIS-PPQ Manuals is available at: http://www.aphis.usda.gov/import_export/plants/manuals/online_manuals.shtml
The one that most affects us is "Nursery Stock Restrictions," which defines those plants or seeds which may enter the US, along with any necessary restrictions and/or treatments (in pdf form): http://www.aphis.usda.gov/import_export/plants/manuals/online_manuals.shtml
Local help - contacts by state:
Each state in the US has its State Plant Health Director (SPHD - pronounced "Spud," for short). Questions about plant or animal pests or diseases are managed from this point, and you can locate your local SPHD from this page: http://www.aphis.usda.gov/services/report_pest_disease/report_pest_disease.shtml
National Plant Board (NPB) members inspect plants and commodities for export so that required phytosanitary certification can be provided, as well as working with industries and the public to prevent development of pest plant problems. http://www.nationalplantboard.org/
Your local representatives may be accessed from here: http://www.nationalplantboard.org/region/index.html
Your state State Plant Regulatory Official (SPRO) is the state-based APHIS representative who performs site/plant inspections, with contact information here: http://www.nationalplantboard.org/member/index.html
Larger context for regulations:
Because plants and seeds are moved around the world, the regulations governing them cannot be created in a vacuum, at the whim of each government.  The International Plant Protection Convention (IPPC) operates under the UN's Food and Agriculture Organization (FAO): https://www.ippc.int/IPP/En/default.jsp
The IPPC is an international agreement, with 177 signatory countries (including the US), with the aim of protecting cultivated and wild plants by preventing the spread of plant pests and diseases.  Country representatives write overarching guidelines, called Standards, that form the basis for all regulations and phytosanitary measures written by IPPC's member countries.  Country representatives to the IPPC may be found here: https://www.ippc.int/index.php?id=1110520&no_cache=1&type=contactpoints&L=0
The country members are also gathered into nine regional plant protection organizations (RPPOs) that address their regional issues.  The United States is part of the North American Plant Protection Organization (NAPPO); the European and Mediterranean Plant Protection Organization (EPPO) covers the EU and other regional countries; etc: https://www.ippc.int/index.php?id=13310&no_cache=1