How to connect to microsoft azure?
what would be my storage account? 


MYCOMPANYbackups


  How can I have access to the backup files?


http://portal.azure.com
or
AzCopy
or
PowerShell
or
Azure Storage Explorer


  Where are these azure permissions managed?


Permissions for accessing the blobs is controlled by the storage account keys, or Shared Access Signatures.  See Azure Storage Security