Cleaning cups

I hope this question isn't too silly, but do you boil your cup in a pot thats specifically used for that purpose? Can you sterilize the cup in a pot you use everday for cooking or would that be unhygenic? It's just that right now I can't afford to buy a cup and a new pot...

edit: Thank you all for your inputs :) I think I might use steralizing tablets - they cost about $6 for a pack of thirty and you dont even need a whole one for each wash. It just seems less risky because I've heard of people accidently dry boiling their cup.