Final steps of data center migration
Below steps will help you :


Create full backup with compression
Ship the compressed backup to the new data center
Configure database mirroring in async mode
When you are ready for failover, change the mirroring mode to sync mode.
Initiate failover to secondary (new data center)
  alter database db_name set partner failover
change the web.configs for your application to the new server.
Follow the steps from my answer - it covers migrating your logins/users/jobs/ssis packages and other post restore steps.



  If database mirroring is on can we start to read/write to the target of the mirror in preparation for turning the target into the primary database.


When you initiate a failover, this is where your downtime is - your application end users will be getting an error and they will be able to reconnect to the new data center database server (provided you have changed the conf setting).

I am assuming that you are using enterprise addition since standard edition of sql server has limitations on database mirroring.

Also, database mirroring is deprecated and you should look into moving to AlwaysON (depending on edition and version of sql server you are using).