If you are NOT familiar with BACKUPs in SQL Server then I strongly suggest you get some reading first [no sarcasm here] on this topic before going ahead with this task.
Understanding SQL Server Backups
SQL Server: Recovering from Disasters Using Backups
Why are you shutting down the database? Are you using SQL Server Express edition? Can you share your SELECT @@version information? Also you need to do Transaction Log backups only if the database is in full recovery model.
select name, recovery_model_desc from sys.databases
If you need help with the actual syntax for your needs then you need to share the data/log file structure a bit.
SELECT name AS 'FileName' , physical_name AS 'PhysicalName', size/128 AS 'TotalSizeinMB',
size/128.0 - CAST(FILEPROPERTY(name, 'SpaceUsed') AS int)/128.0 AS 'AvailableSpaceInMB',
CAST(FILEPROPERTY(name, 'SpaceUsed') AS int)/128.0 AS 'ActualSpaceUsedInMB',
(CAST(FILEPROPERTY(name, 'SpaceUsed') AS int)/128.0)/(size/128)*100. as '%SpaceUsed'
Some additional BACKUP & RESTORE commands from BOL.
If you need additional help, don't hesitate to ask but share clear details.