I bought this plant from a home repair store 3 days back, but I don't know what it is. Now it seems that its decaying. What is this plant and what do I need to do to take care of it?
It is a begonia, probably a Rieger begonia. Check this begonia care site for details.
Begonias commonly get gray mold (Botrytis). Since this fungus moves from dead tissue into living, pick off any dead flowers or leaves as soon as you can. Try to keep the foliage and flowers dry.