You are going to want to do some searching on "Lerp" which is a math concept that allows you to move an object over time with a nice start/end speedup/slowdown effect
but basically it will be
On "DestinationObject" clicked ->
(Sub event)Every Tick -> "object that needs to move" set position to
X = Lerp ( "object that needs to move".X , DestinationObject.X , 0.5*dt)
Y = Lerp ( "object that needs to move".Y , DestinationObject.Y , 0.5*dt)
If you play with the value 0.5*dt you can make it faster/slower - eg: try 0.3 or 0.7