This depends on the structure and design of your application, which may require a custom process. We have two potential release processes and a patch process, all initiated through our web or email case submission system:
a) We copy your production environment into a test environment. You, the customer, release code via scp/ssh into the test environment and test it.  When the testing is complete, you notify us and we alter the IP addresses to make your test environment be your new production environment.  We rsync any changes to the live site data from the old production environment into the new one where appropriate.  In this case, there is no code transfer to ENKI's organization, simply a "pointer change."  This works well when data doesn't need migration.
b) We copy your production environment into a test environment.  You release code yourself via scp/ssh into the test environment and test it.  You generate a patch process describing what you did to successfully install the update and do any migrations.  On your request, we stop the production environment, give it temporary IP addresses, and perform your documented installation and migration process for you, and run any necessary tests or give you time to do so.  When the tests pass, you inform us through a case submission, and we alter the IP addresses of the production environment to their normal DNS values.
c) For simple patches, you notify us by submitting a case, and provide an scp server with the patch on it, together with patching instructions. We perform the patch and restart the live site.

Other processes can be created to meet your needs.