Implement this code on the worksheet you want it to work on (right click on the worksheet tab, click on view code):
Private Sub Worksheet_Change(ByVal Target As Range)
ActiveCell.Offset(-1, 1) = Time
Whenever you put something in a cell and hit ENTER, the current system time is being put in the adjacent cell to the right.
NOTE that you have to confirm your entry by hitting ENTER and not use the arrows or TAB.