I was born in the USA, my dad was born in Switzerland. Can I get dual citizenship or a Swiss passport?

Yes! You can get a Swiss Passport, Making you a dual citizen of both USA and Switzerland if your Dad who was born in Swiss has a Swiss citizenship. This means that either or both of his parents were Swiss. The law in Switzerland does not make a person an Automatic citizen by virture of being born in Swiss, unlike in USA. My dear, find out from your Dad if he is a Swiss citizen. If he is, then go to to the nearest Swiss embassy to you and file in the paper work...
Regards!