Probably the easiest way to get to Morzine is by plane. There are loads of flights going from all around the UK to Geneva, the nearest airport. Try Easyjet, or if you're travelling from Scotland, FlyGlobeSpan fly from Edinburgh and Glasgow.
Flights don't take long at all and all you have to do at the other end is get a short (45 min) transfer up to the resort.

It is possible to get to Morzine by train. Trains from Paris and Geneva arrive several times a day at Thonon station. From there buses serve as a link up to the resort itself (40km from the station)

A lot of people drive to Morzine. It takes roughly 11 hours to drive (550miles, 850km) from Dover. You can drive on the motorway as far as Cluses, from then on its only 35km from Morzine.
Taking you car to Morzine means you can easily get up into Avoriaz or to the shops. Parking is free in the main Morzine car park.
If you're doing a season its also good, you can get to the places known for the good powder dead early for first tracks and its so much cheaper to head down to the main supermarkets in the valley.
Have a look at The RAC for more details of how to drive there.