Using Combobox in DataGridView

I have a DataGridView that is bound to a SQL-Server database, and it works fine. One column, however, contains the key value for a record in another table... entering "1" doesn't mean very much, you know? So I want to add a ComboBox to the DataGrid that lets the user choose the Name while the grid saves the key value.

For example, let's say I'm building a list of students in a class... I have two tables: The first table contains a list of students, and the second places those students in a particular class. Instead of storing the student information directly in the second table, I want to store the student ID... but I want the combo box to DISPLAY the student's name.

Does anybody know how to do this, or can point me to a good source online that will show me how?

Thanks.