With data grid views you can edit the values in cells directly using the control on the form, and it should automatically update the DB if it's data bound.
To edit programmatically, if you know the X and Y positions of what you're trying to retrieve/edit, you can use:
object obj = myDataGridView[X, Y].Value
myDataGridView[X, Y].Value = obj;
This will allow you to access the value directly.
However, you can't always explicitly state what you want to retrieve. If the user selects a row on the data grid view you can use:
DataGridViewRow row = myDataGridView.CurrentRow
DataGridViewCellCollection cells = row.Cells;
object obj = cells["ColumnName"].Value;
object obj = myDataGridView.CurrentRow.Cells["ColumnName"].Value;
myDataGridView.CurrentRow.Cells["ColumnName"].Value = obj;