There's no good way around it - Tignes is a fair old way away from major traffic routes and airports. It's part of what makes it attractive as a ski resort - high glacier skiing in the middle of the mountains.
Having said that, connections have improved steadily over the years and the journey from the airport or up from the motorway through Moutiers and Bourg St Maurice is no longer the endurance test that it once was.
Travel by Car
Geneva 173km - find the way out of the city onto the A40 to Annecy, then follow the road along the lake to Albertville and into the Tarentaise valley
Lyon 239km - probably where most people come to if travelling from other parts of France. Look for motorway routes A43 & A430 to Albertville, then as above.
Chambéry 134km - a shorter version of the route from Lyon above.
Travel by Air
As can be seen from the map above, the closest airport is Chambéry, which is used by a number of low-cost carriers and some of the British package holiday operators. The traditional option was always Geneva, with a massive amount of choice of flight destinations and both scheduled and charter traffic. Grenoble originally served the more southerly resorts but is becoming somewhat popular with the Tarentaise resorts - again it offers mainly low-cost flights and charters from the UK. Lyon is the second choice as far as the number of options available, again with a good mix of charter, low-cost carriers and scheduled flights.
Chambéry-Savoie Airport (a few kilometres to the north of Chambéry) - 135km
Geneva Cointrin International Airport (a couple of kilometres to the north of Geneva) - 180km
Grenoble-Isère Airport (located some distance to the northwest of the city) - 215km via Grenoble and Albertville
Lyon Saint-Exupéry International Airport (a few kilometres to the east of the city) - 240km via Chambéry
Travel by Rail
Tignes has no railway station - the closest is at Bourg-Saint-Maurice 30km down in the valley. There is a TGV service to Bourg from Paris which connects with the Eurostar service from London. Eurostar offers a Direct Ski service during the winter season which runs from London St Pancras. Once at the railway station there is a regular bus service up to Tignes run by Altibus from early in the morning to late at night as well as taxis from the town.
Altibus - bus services from Geneva, Lyon and Chambéry airports and Bourg-Saint-Maurice train station. The site offers PDF timetables for the various destinations.
AeroSki Tarentaise - this is the regular bus service between Geneva airport and the Tignes villages. Again with a PDF timetable available for download.
Eurostar - offers train timetables for direct rail from London to Bourg St Maurice