By default, when the Tab key is pressed and a cell is not being edited, the next control on the form will gain focus. If a cell is being edited, the cell that is being edited will exit edit mode and the next cell will gain focus. 

If you want to navigate through the grid using the Tab and arrow keys, but remain in edit mode, you will need to handle the grid's KeyPress event to handle the Tab and arrow keys and call the appropriate cell's EnterEdit method.