Create a cell with the value Now().
Format it how you want - like yyyy/mm/dd HH:mm:ss for a full timestamp in 24 hour time.
Now, as long as auto-recalculate (the default) is set, any time another cell is changed, you'll get a fresh timestamp.
Upon further reflection, if you desire a hardcoded timestamp, which is only updated by actions not including such things as open workbook, print, etc. you could create a macro attached to worksheet_change. Set the target cell as text, with specific formatting like before. Use something like:
Sheet1.Cells.Value = Text(Now(), "yyyy/mm/dd HH:mm:ss") on the Worksheet_Change event.
If you put this into a template that loads at startup, you'll never have to think about it again.