You can use the CurrentCellChanged event to detect when the currentcell changes position. But this event will not allow you to catch the start of a cell being edited.
One way you can do this is to catch the TextChanged event in the embedded TextBox within the cell. If the text changes, then it might be the beginning of a cell edit provided the text in the TextBox differs from the stored value from the DataSource. The reason you need to check for a different value between the grid DataSource and the TextBox contents is that the TextChanged event is fired initially when the TextBox is initialized when the cell becomes current and moves the value from the grid ataSource to the TextBox. You also have to ignore subsequent hits of TextChanged as the same cell continues to be edited. Here is both a VB and C# sample that implements this strategy to flagged current cell start editing.