The nearest airport is Geneva Airport (GVA). From there you can take the train to Martigny and then transfer to another train to Le Châble. From there you can reach Verbier by gondola or Car Postal (bus).
The festival will also be running a free local shuttle bus service for festival-goers with stops at Périn, Place Centrale, Brunet, Savoleyres and Carrefour. These will run every 5-10 minutes on Thursday from 15.30 to 03:00, on Friday and Saturday from 11:30 to 03:00 and on Sunday from 11:30 to 22:00.
Polaris Festival is an 18+ event. You may be required to show ID upon entry.