You could use a button that would loop through the data in
the grid and submit it to the database as an upadte. Or use the
change event to process that cell and update as the user types.
Either that or the keyup event should work.
Since you are want to edit the cell, you should use
itemEditor="mx.controls.TextInput" along with
editorProperty="text". But if you are using TextInput, then just do
editable="true" on the DataGridColumn as TextInput is the default
editor for the cell and save yourself some work.
The changes are stored in your dataProvider, so following
Diemos's advice, loop through your dataProvider to build your
request back to the server. Although what you build greatly depends
on which data service you are using. For example, if you are using
RemoteObject, then you might be able to send your dataProvider
as-is. If you are using a HTTPService, you may need to send an XML