Euh... where are the Pyrenees?

The Pyrenean mountain chain runs roughly west-east from the Atlantic Ocean to the Mediterranean Sea. They separate France, to the north, from Spain, to the south. The principality of Andorra is a mountainous enclave in the middle.

What's the best ski resort?

St Lary. It has everything - a real village, cafés, clubs ... and great skiing. The ski domain at La Mongie is very good, very extensive ... but for accommodation of any style you have to go down to Bagneres or Bareges.

How do I get there?

By plane your best bet is Toulouse which is served by Air France, BA, Easyjet, Flybe and many more. Then there's Pau, Biarritz, Carcassonne and Perpignan which have regular flights from Dublin, London and Liverpool - by Ryanair.
By train, the TGV (high-speed train) gets you to Toulouse from Paris in 4 and a half hours and then local trains can shuttle you into the mountains in 40 minutes or so.
By car ... Toulouse is 7 hours from Paris. Take the new A20 motorway via Orleans, Limoges and Cahors - it's much cheaper than by Bordeaux or Clermont-Ferrand in terms of tolls.

What's there to do in summer?

Hiking, climbing, trekking mainly with a range of more extreme sports/occupations also possible: rafting, canyoning, parapente, downhill scooter racing (yes!) and lots more.

Where should I stay?

Try using 'gîte d'étape' - sort of mountain hostels which line the Pyrenean footpath, the GR 10. Not to be confused with 'réfuges de montagne' which are high-mountain huts of rudimentary comfort but Oh! so welcome when you're dying on your feet. A good 'gîte d'étape' is La Girada in the Eastern Pyrenees.