I am planning to write a Java applet for Tower of Hanoi similar to link( http://www.mazeworks.com/hanoi/index.htm ) Can you suggest how should I start and proceed.
And, btw, does it require multi threading?
And also, major part of my doubt is
to make a disc being clickable and being able to drag and drop the disc on a tower.
detect a tower (if a disc is being dragged using mouse)
To answer the multi-threaded question, all GUI applications are multi-threaded (or have to fake it - but in the case of standard Java GUI stuff, they're all multi-threaded). That's because they have to deal with events, including repaint requests and such as well as user input. The algorithm itself shouldn't require multiple threads, and you shouldn't have to do a lot with threads (it'll primarily be a case of implementing the proper event handlers), but you're definitely going to have multiple threads for an applet.
I would start with this http://www.rstack.com/hanoi/hanoi_src.html or http://stud1.tuwien.ac.at/~e9125168/javaa/jtower.html. As far as threading see my comment on Jonathan M Davis's answer.