Have a look at the apply page:

Apply

You must apply online for an EEA family permit.

That link directs you to Apply for a UK visa, which includes the following:

Apply for all other visas

Apply using the Visa4UK service for all other visas, including if you’re applying:

• to live with a family member already in the UK
• to visit your child at an independent fee-paying day school
• to set up or run a business in the UK
• for a UK ancestry visa
• to prove you’re allowed to live or work in the UK without any immigration restrictions (called ‘right of abode’)
• for an official visit or for diplomatic business
• for a visa to prove you’re exempt from immigration control

That should get you started. Even though the Visa4UK list does not include EEA family permits, the site does include them.

The Visa4UK service is not the easiest to use, however. If you need help filling out the online form, you may find it here, or you may find it at Expatriates, since the family permit may be used for short visits, for longer stays, or for permanent immigration.

Your application will probably be refused unless the two of you have lived together for two years or longer; that appears to be one of the criteria used to define "durable partner." Since the application is free of charge, though, you may want to try even if you have been living together for a shorter period.