Check out the railway Deutsche Bahn
. It's only 4 h from Frankfurt to Zurich. There are reduced fares when you book a train in advance (up to 50 %), but only on specific dates and trains (you can only use the train you booked, otherwise the ticket is invalid). The cheapest tickets would be online booking under "Offers Europe", then "surf & rail" (39 € one way). You could also go to Frankfurt main station, and next to the ticket office (Reisezentrum), there is a railway travel agency, DB Reisebüro, where you could get info and book trains and hotels or package tours.
The Swiss railway net is great, and a very convenient way of seeing the Alps is the Glacier Express
. You could go from Zurich to the starting points Chur or Davos (a nice ski resort) and then all the way to Zermatt.