The idea is to have 2 states, one waiting for the mouse button to be pressed, and one waiting for it to be released.
State 1 (wait for mouse down) transitions to State 2 (wait for mouse up) which transitions back to State 1.
In State 2 you just use a Mouse Pick or something and get the position, then use Set Position to put the object at that position. Get Mouse Button with Bool Test will get the transitions working for you. Use a 3rd state with Next Frame Event if you get infinite loop errors. The movement/following would depend on how you want it setup, but thats basically all that is involved.