Geneva airport is serviced by most major Airlines including Easyjet who run several flights a day, BMI Baby and Speedjet.com an now a new service in 2006 Globespan. My family used the latter and found the service excellent the only draw back is they fly out of Manchester which is a bit of a trek for us.
From Geneva airport you can either hire a car or travel by train.
St Luc is situated 2 hours from Geneva by car. Simply follow the Auto route from Geneva to Lausanne then to GD.St Bernard then Sion and Sierre when the motorway stops just after Sierre turn right to St Luc.
The train is a good option, it will cost about £45 return, the train leaves form Geneva airport to Sierre and trains run about every hour with the journey taking approximately 2 hours. It is then possible to catch the 'Post Bus' to Vissoie and taxi or bus to St Luc. It is possible to fly to Sion airport which is only 45 minutes from St Luc but currently only Swiss fly there from London Heathrow and the flights are quite expensive.
By
Car
I have done the trip many times in a car, a car with a trailer and a 7.5
ton lorry. Using the channel tunnel (check out frequent traveller fairs
for a very good deal eurotunnel)
it is possible to do the trip in around 12 hours from the midlands to
St Luc. Direction are Calais, Reims Dijon, Geneva, Lausanne, Sion, Sierre,
Vissoie, St Luc.
If the roads
are good I would go Reims, Dijon , Besancon, Luasanne this will save about
90 km but the road does rise to 1000m so it could be affected by snow.then
follow directions to GD.St Bernard then Sion and Sierre when the motorway
stops just after Sierre turn right to St Luc.
The road to St Luc is not for the faint hearted, it is 21 km from the
motorway and takes 35 minutes in good conditions in snow chains are essential.