SQL Server Database Migration - Backup/Restore while Original DB still in Production
First step is to change the recovery mode to FULL.

Take a full backup (with compression), and restore the full backup to new server with NORECOVERY. This will allow you to restore additional log backups.

Now configure logshipping from the primary (old) to secondary (new) server.

During the time of cutover, take a tail log backup and bring the secondary server online by restoring the log backup WITH RECOVERY.

make sure you have instant file initialization enabled on both servers to cut down the restore times.

Refer to my answer for Moving Databases to New Datacenters for more detailed steps.