You can use Database Back Up and Restore function for this task without any problem. However, there are couple of error messages that you have to aware.
1. Back your database from the Original location (Server A)
2. Copy it to the new location (Server B)
3. Create a instant of a database in Server B and restore the backup copy that you took from server A
Yes, it is a quite simple process. Lets handle couple of error messages you might have to face while you trying to copy the database to new location.
Error Message: The backup set holds a backup of a database other than the existing
Solution: Go to Options page (Restore Database) and check the Overwrite the existing database option.
Error Message 02: System.Data.SqlClient.SqlError: Directory lookup for the file
Solution: In the options Page (Restore Database) check the Restore the database files as: pane. If your new server is 64 bit it might still looking the files in Program Files folder but actually SQL is installed in Program File (x86). Select the correct path.
Error Message 03: System.Data.SqlClient.SqlError: Exclusive access could not be obtained because the database is in use. (Microsoft.SqlServer.Express.Smo)
Solution: Open the SQL Server Configuration Manager and restart the SQL Server.