The answer depends on whether you are using the current two-factor authentication, or the older two-step verification.
If you are using two-factor authentication you need to plough through the processes described in these pages:
Two-factor authentication for Apple ID - Apple Support
If you forgot your Apple ID password - Apple Support
There is a contact link for Support at the bottom of the second page linked to.
If you are using two-step verification (which would have been set up several years ago) you need two out of three things to get into your account: your password, your trusted device to receive a code, or your recovery key. If you have lost two out of these three things I'm afraid you are permanently locked out. (You should still contact Support in case anything has changed about this since the original information, but don't get your hopes up).
Two-step verification for Apple ID - Apple Support