how to save the datagridview items into the database using csharp

I wonder firstly how you have loaded the data in the datagridview. If you've loaded it using the data provider for ole db for example, then any changes you make will be to the dataset you've loaded. you then need to create an sql command to 'action' those changes in the database.

This is a good starter for the code you should look at further. Depends where you're database sits, i.e. Access, SQL server etc as to which you implement.

http://msdn.microsoft.com/en-us/library/dw70f090.aspx#_OleDb

HTH