$40 flight from Sweden to Italy? Move over, Eurail pass!

I felt slightly scrunched on my Ryanair flight, but I didn't mind. I was heading from icy Stockholm to sunny Rome just three days before Christmas, and I'd paid a mere $40 for the trip. When the silly applause soundtrack played upon landing -- something I'd gotten used to during my many low-cost, country-hopping flights -- I was inspired to clap along. After all, my winter-trodden soul had been uplifted for a fraction of the cost and time a train would have required.

Many people still use rail passes to get around Europe, but for those willing to put up with a few idiosyncrasies -- such as advertisements over the speaker system -- there's a much cheaper option: discount airlines.

Low-cost carriers took off across the Atlantic in 1990, when Ryanair modeled flights after the discount concept pioneered by Southwest Airlines, according to the International Air Travel Association. In the past decade, their market share has jumped from 9 percent to 39 percent in Europe, with budget airlines carrying 46 million people on more than 500 routes annually.

Admittedly, flying cheaply is not without its hassles, but discount flights can transform a tour of the continent from an impossibility to a reality. After taking many discount flights during six months in Europe, I learned that the payoffs were worth the pitfalls -- provided you know the ropes. Before you fly on Ryanair, Easyjet and other similar carriers, heed this advice.

Understand how they work

Unlike major carriers with many routes, discount airlines offer limited destinations with no connections. At the carrier's websites, check to see what direct destinations are possible from your originating city. Your starting point will make a difference in how many destinations you can easily access. Dublin and London boast far more discount connections than Nice, France, or Munich, Germany, for example. When you choose a target and a date, the airline will show you the available flights to the destination during that week, the prices, and separate fares for the departing and returning flights.

Fares are advertised in the currency of your departure city. A good site to check currency conversions is XE (www.xe.com).

Start your search with Ryanair (www.ryanair.com) and Easyjet (www.easyjet.com), based in Ireland and England, respectively. They have the most connections and the most reliable service.

For flights to Eastern European locations such as Warsaw and Budapest, check WizzAir (wizzair.com).

German Wings (www. germanwings.com) and AerLingus (www.aerlingus.com) are not consistently as cheap as others, but can offer a deal.

The best overall flight site I found was SkyScanner (www.skyscanner.com), which is similar to Priceline, but includes discount airlines. The site will construct routes with connections using a variety of discount airlines, but beware: When booking multiple legs through discount airlines, you'll likely encounter horrendous, even overnight, layovers. Your bags will not transfer. You increase your risk of a canceled flight that could leave you stranded, and any missed flights will likely not be rerouted or refunded.

Keep a watch out for fees

Flying cheaply requires careful avoidance of fees.

Be sure you book the right day and time and use the correct name, because making changes after booking can double the cost. I booked a round-trip flight for three from Oslo to Dublin at $60 per person ($180 total), and had to pay $170 more after I realized I booked the return flight on the wrong day.

Every step of the booking and flying process will be filled with offers for insurance and upgrades. One wrong click, and your discount is no more.

Study up on airports

Discount airlines fly into and out of airports that are sometimes an hour or more by bus from the advertised cities. Ryanair flights to Frankfurt, Germany, land about 75 miles outside city limits in Hahn, for instance. Before you book, check the transportation options to departure and arrival airports. It might mean a short $2 train trip -- or a $40 to $50 ride on a bus whose company has a monopoly on transportation from that airport.

Decide if you want to check a bag during your booking; if you change your mind later, you'll get smacked with a $50 fee. If your bag is too heavy, you could find yourself paying $200 or more -- and lamenting: It would have been cheaper to fly a regular airline.

Equally onerous: You get one carry-on. Not a carry-on plus a purse or laptop. One bag. Everything has to fit. (Or, like I did, you can wear a huge coat with bags underneath it, hoping that airport officials won't wonder why one of your hips sports a protrusion about the size of a camera carrier.) Also, that bag may need to fit into a basket designed to check its size. Bulging bags may be singled out. It doesn't fit? Check it for $50.

In some cases, friends and I walked right onto the plane without anyone weighing my bag or checking its size. When a friend was stopped for an overstuffed bag, however, she was allowed to rearrange -- and wear -- its contents. She put on every article of clothing she could stand until her bag was the right size and weight.

Forget peace and quiet

Every moment you feel yourself floating toward sleep will be interrupted by loud, enthusiastic commercials from companies whose obnoxious advertising likely made your cheap flight possible. A catalog with items for purchase will sit snugly in the seat pocket before you, though you likely won't have time to leaf through it between the flight attendants' sales pitches to buy smokeless cigarettes, liquor and perfume.