Websites like travelocity.com and orbitz.com are good places to start, but you'll have to dig deeper to find the best deals. When airfares to the UK are on sale but Geneva, Zurich, or Milan are expensive, consider flying to London and hopping over to the mainland on ultra-cheap carriers EasyJet (easyjet.com) or Ryan Air (ryanair.com). Tickets to Turin, which is close to Alagna, start at $1.85 plus taxes (yes, $1.85); to Friedrichshafen, Germany, an alternate gateway to St. Anton, they start at $3.95 plus taxes.
You can also find remarkable deals on the websites of major European airlines (British Airlines, KLM, Lufthansa, Swiss, etc.). Scandinavian (scandinavian.net) tends to be one of the best-in wintertime, it offers two- for-one deals to most major European cities. If you're extremely flexible, Airtech (airtech.com) can get you to Europe for $199 one-way.
And, finally, if you're a student or under 26, check cut-rate fares from STA Travel (statravel.com).
Powder: For weather reports, past and future, check snowforecast.com. The website is easy to navigate and has snow-specific forecasts for resorts around the world.
Timing: Don't jump the gun. The Alps receive at least twice as much snow in February and March as they do in December and January. Communication: Your American cell phone likely won't work here, but rentals (from $50 a week) are available in all major airports. Dial 112, Europe's equivalent of 911, to reach emergency services throughout the EU.