how can database snapshot to be used to recover data? I know the logic behind database snapshot and how it works.
But my problem is how can database snapshot to be used to recover data? 
can we take a backup of database snapshot and restore it in a new server?

I am using MS SQL server

Thank you.
how can database snapshot to be used to recover data?

Yes, you have to use restore database ... FROM DATABASE_SNAPSHOT. It is called reverting the database to a database snapshot. You would use it to reverse a serious error e.g. drop table, deleting data, etc.
This is important :

all changes made after the snapshot was created are lost.

.

can we take a backup of database snapshot and restore it in a new server?

No, you cannot. This is covered in Database Snapshot limitations


You cannot back up or restore database snapshots.

You cannot attach or detach database snapshots.



Very important :

Using database snapshots for reverting a database is not a substitute for your backup and restore strategy. Performing all your scheduled backups remains essential. If you must restore the source database to the point in time at which you created a database snapshot, implement a backup policy that enables you to do that.