To get to Aime 2000 from Plagne Centre you can take a cable car Telemetro. It works till 1 am so you can stay in Plagne Centre for the Apres Ski party and I bet you will find Telemetro very helpful then.
It also comes in handy when you go down from your hotel on the sleigh at midnight. But you better not trust French people that they will keep it open till 1 am and don't go down at last minute. They tend to close it few minutes before and there is no way they will let you in. The only way to go up is walking or hitch-hiking then.
The closest airport is Chambery-Aix. In the winter, quite a few cheap airlines, including Buzz and Excel, fly direct to Chambery.
Direct flights from the UK include London Stansted, Newcastle, East Midland, Leeds Bradford.
Direct flights from Sweden include Malmo and Stockholm.
Note however that getting from Chambery airport to anywhere is not necessarilly easy. If you haven't arranged transport with your tour operator (assuming you've got one), the cheapest way is to take a taxi to Chambery's train station and take the train to Aime. This should cost you 20 euro for the taxi and 12.50 for the train.
Aime has a small train station and the French high speed train, the TGV, stops there. This is definitely the quickest way to get to Aime from Paris or Lyon.
Now, more interesting is the fact that, in winter, you have special Eurostar trains coming directly from London that stop at Aime as well.
From the station, you can get on a coach to go up to La Plagne. It will cost you 8.20 euro to do so.