Getting There:

Saas Fee is an approximate 35 minute drive from the main auto route running along the valley from Switzerland through to Italy.  By car it is approximately 2 hours 20 minutes from Geneva or Milan, slightly further from other Swiss Airports.  The Swiss rail system to Visp or Brig is very good and a 35 minute taxi ride (about 60 CHF or 120 CHF for full minibus for your family and luggage) or much cheaper transportation by the regular Saas Fee buses will bring you straight into Town. There are no-change train routes  direct from Geneva Airport to both Visp and Brig - these tun every hour and are very reliable. There is a brand new train tunnel which has shortened the journey from Zurich Airport dramatically and this journey to Visp is now typically less than 2 hours

The Swiss public transport system is extremely good and a truly relaxing way to travel but car hire gives you a little bit of flexibility and will cost you in the Region of ?35-60 per day depending upon the vehicle.
If you are a family travelling in Switzerland more than once per year by rail, it will almost certainly be worth your while considering a family rail card which can huge reductions even on first class travel.

The tourist office in Saas Fee on www.saas-fee.ch or the rail service on www.rail.ch are two very helpful websites with all sorts of information

If you wanted to consider a one way car option from one of the airports you probably would want to look at Europcar because they have a local drop point at a garage in nearby Visp

If you fly by Swissair remember the possibility of the bags through system - they will take your bags at check in and you dont need to see them again until you get to the chalet - they can be transported all the way through if you wish