The DataGrid actually auto-handles right, left, up, down arrow keys. That being said, you can move the cell focus around using any of those keys and then start typing to get into the edit mode (iff the cell is editable). You don't have to listen to key press down events. Note that if you hit "Enter", then you will move to the next row.
EDIT:
Of course, by default the arrow keys won't put a cell into edit mode. Instead, you have to type in stuff or use the mouse pointer. But, you can do the following:
private void myDataGrid_CurrentCellChanged(object sender, EventArgs e)
{
myDataGrid.BeginEdit();
}
This will force the cell on focus to enter the edit mode. I tried using key event handlers, but it seems the DataGrid won't let the user listen to the arrow keys and Enter (although you could if you use WIN32 API). Now, whenever you use any of the arrow keys, the newly selected cell will be in edit mode. Try hitting Esc to escape this mode.