More than likely, you need to take it to a machine shop to get the work done. Or, you could try to do it yourself with an EZOut extractor.
Let's see... alot of automotive places such as Advanced Auto, Auto Zone, Napa, Pep Boys, and also most of your local hardware stores should have EZ-outs... also Snap-on, Sears (Craftsman), and Cornwell produce these also
A RENCH................GENIOUS!! The broken screw will have to be replaced. A loose alternator belt will not recharge the battery - might also cause the engine to overheat if it is the same belt that drives the radiator fan and water pump. If the screw is broken inside the alternator, you can reverse-drill it out with an EZOut or you can just drill it out and replace with a bolt and nut. Other solution would be to buy another alternator. I don't know of any way you can tighten it temporarily except for maybe using a wooden wedge between the alternator and the alternator bracket or by using a piece of wire to hold it as far back as you can on the bracket. But these are emergency and temporary techniques - not a solution.