Mirroring SQL 2008 R2 database
I have just started as a DBA 


Solving problems using Backup and Restore is the bread-and-butter of a DBA.


  move a 4TB database from a physical server to a virtual server with little down time. 


Define "little".

The safest, simplest thing is to leave the database in Simple recovery, and use Full/Differential backups to move the data.  

You can also switch to Full recovery and use Log backups instead of Differential backups.  

In both cases you would

1) Take a Full backup

2) Restore the Full backup on the new server WITH NORECOVERY

3) Begin Downtime

4) Take a final Log Backup or Differential Backup

5) Restore the all the Log Backups or the Differential Backup WITH RECOVERY

6) Set the database OFFLINE on the old server

7) End Downtime

You can perform steps 1, 2, 4, and 5 as many times as you want in testing, and to measure the required downtime.