You can do this using a relative position and place referenced to that, or you can place using the Type Offset or Type Coordinate commands from the context menu.
To change the relative origin, select the reference item (a pad for example), and from the context menu, select Origins and Set Relative Origin At Item.  will move the cursor to the origin of the selected item, then will place a relative origin at the cursor. 

The status bar will change to display Rel (instead of Abs), this indicates that you are in Relative coordinate mode.
All movement and pad positions will now be relative to this position.
Sometimes it's desirable to offset the absolute origin from the bottom left corner.  The simplest way to do this is to set a relative origin, then go to [Settings], [Units].  Copy and paste the co-ordinates from the bottom pair of boxes to the top pair and the absolute origin will be set at the relative origin position.  This is also the place to correct any slight errors in the placement of the relative origin.