My father in law drinks sweet vermouth on the rocks before dinner and it's actually not so bad (I guess I just like drinks before dinner).
If you like bitter cocktails, try a Negroni : 1oz gin, 1oz campari, 1oz sweet vermouth.
Manhattans also use sweet vermouth (with whiskey and bitters)- pretty tasty.
Dry vermouth is used in a Martini with gin. Some people like just a drop and some a little more. It's not so good on its own. You can use it in cooking as well and it keeps for a looooong time.
But, I don't know what it is.