To integrate Apple's Device Enrollment Program (DEP) with eSpark's Orchard MDM, partners must upload the Orchard public key to Apple's servers and provide eSpark with Apple's DEP token. This involves generating a new token in Apple's DEP portal, downloading the token, logging into Orchard, downloading the Orchard public key, uploading the DEP token to Orchard, and returning to Apple's DEP portal to replace the key with the one from Orchard.