Simon Calder: The Man Who Pays His Way

"This is Chicago. Doors open on the right." The pre-recorded announcement is friendly – and perilous. "Thank you for travelling on the Blue Line" may be the last thing the newcomer to the Windy City hears before emerging above ground and realising, from the scene of dereliction and faint air of menace, that something has gone badly wrong.

Chicago has one of the best urban railways in the world. The "El", as the city's elevated and underground railway system is known, is visitor-friendly in many ways. From the city's two main airports you can reach any station on the system for just $1.50 (£1). Tourists in London must cope with complicated names like Central, District and Bakerloo, and translate these to the colours on the Underground map; in contrast, lines in Chicago are simply named Red, Green or Brown, for example.

Much of the system is high above the streets, giving startling views of the city; and in a place where the temperature sinks to minus 18C and Lake Michigan becomes a sheet of ice, many above-ground stations have open-air heating in winter. But whoever chose the names for the stations did the traveller no favours.

When you travel by train from the world's busiest airport into the city, and an announcement says "Next stop, Chicago", you may be tempted to gather your belongings and companions together and prepare to get off. But on the way in from O'Hare, Chicago station is where Chicago Avenue happens to cross the Blue Line. It is several miles from the dramatic, beautiful and safe centre of America's third city. "Chicago" is the name of a station in an deprived area where some malevolent residents welcome baggage-laden tourists.

Even if you correctly decided to stay on the train and make it into the city, your navigational problems are only just beginning. The system has not one Chicago station, but three – besides the Blue Line, the name pops up on the Red and Brown Lines as well. Three other station names occur in triplicate: Addison, California and Harlem. It gets worse: the appellations Pulaski and Kedzie are applied to four stations apiece, while Western has no fewer than five manifestations – three of them on the Blue Line alone.

London's Underground may be slow and expensive, but at least when Ruislip appears in five station names, there is a "Gardens", "Manor", "South" or "West" to help you tell them apart.

On Chicago's south-western railway, when you arrive at Midway, you are halfway to the end of the line, right? No, you have reached the terminus – or terminal. Midway is the city's second airport. Here, you can tell Northwest from Southwest by looking at the price on your eastbound ticket.

The woman at the Northwest Airlines counter glanced at the screen and shook her head. "Because you're booking on the day of travel I can't offer you any breathtaking deals." She was wrong: when she quoted the price, I gasped. For the 90-minute flight from Chicago to Boston, Northwest's fare is $751 (£500). "Try Southwest," she suggested conspiratorially, and pointed to the north end of the terminal at Midway airport. The rival airline wanted only $181 (£120) for a flight to "Boston Area", a euphemism for the city of Providence, across the state line in Rhode Island. I was content to arrive 60 miles away from the Massachusetts capital in return for paying only a quarter as much as Northwest wanted, and for travelling on the safest airline in the world. After 10 million flights, Southwest has yet to suffer a fatal accident; a good average for other airlines is one every million or two departures.

One happy consequence of this remarkable record is that Southwest's cabin crew are confident enough to take liberties with the pre-flight safety briefing. Ojay, the lead flight attendant, began his performance with a theatrical "Your seat belt opens like this – shazam!" and continued with the information that, "In the event that this flight becomes a cruise, your seat cushion will act as a flotation device".

When describing the oxygen system, the Southwest spiel explains, "We never anticipate a sudden change in cabin pressure, or we wouldn't come to work." Ojay ended: "The flight attendants will now pass through the cabin making sure that your baggage is correctly stowed and that your shoes match your outfit."

The entertainment continues inflight, with the invitation to buy "beer and cheap wine for $3". On landing, Ojay let out a yelp of camp astonishment – "We're here!" – and advised everyone that, "Those guys up front fly much better than they drive, so stay in your seat with your buckle fastened until we reach the terminal."

Reaching the terminal was simple. Reaching Boston was trickier. Southwest claims that Providence is "A better way to Boston". That depends on how you define "better". At Providence airport, anyone hoping to reach the Massachusetts capital begins on the wrong side of town. In the unlikely event that a bus into the Rhode Island capital should Providentially show up, Boston is a further hour's ride by clattery old train. In contrast, Boston's real airport, known as Logan, is a couple of miles from the city centre, accessible by underground in 10 minutes, or, more atmospherically, by boat.

Buzz passengers are this week getting used to the idea that "A better way to Frankfurt" is via the US Air Force base at Hahn, and that RAF Laarbruch, on the Dutch border, makes the perfect approach to Düsseldorf. This week, Ryanair announced that its latest plaything, Buzz, is to be shut down for the month of April, while two-thirds of Buzz staff are sacked and 100,000 pre-booked passengers are let down. The no-frills airline that KLM began is losing a million euros a week, even more than the wages of Michael O'Leary, boss of Ryanair, who picked up Buzz for what he describes as "petty cash".

Airlines go bust frequently. Indeed, a regular cull of carriers – while sad for the staff involved – helps to keep the rest of the aviation industry on its toes, controlling costs and offering better fares. With Buzz losing €1m (£650,000) a month, and flying its planes less than half full, Mr O'Leary could have merely waited for KLM to shut down its ailing subsidiary, and then joined the feeding frenzy for its staff and slots at Stansted.

Instead, Ryanair has chosen to buy a near-bankrupt carrier that, it says, "suffers from a number of terminal structural problems including an inappropriate, mixed aircraft fleet". That fleet is incompatible with Ryanair's existing planes. In addition, Mr O'Leary has upset everyone from Buzz's cabin crew and loyal passengers to expatriate Brits who had bought property around Bergerac in south-west France on the basis of year-round flights from Stansted; those have now been scrapped, along with 11 other routes.

Why infuriate so many people? Mr O'Leary's main interest in Buzz is neither the planes nor the people. He has bought a piece of paper.

Ryanair is an Irish airline, which enables it to fly freely within the European Union. Once outside the EU, a new and complicated set of rules comes into play: each country negotiates with Britain about who can fly in or out. As a UK airline, Buzz comes with a British aircraft operator's certificate. This is the essential document for anyone hoping to fly to the "New Europe", an area barely touched by no-frills aviation. As I write, airports along the Dalmatian coast of Croatia and in western Poland are painting the destinations boards reading "Stansted" in eager anticipation of Ryanair – sorry, Buzz – landing. There is even talk that an old military base somewhere in Bohemia is being redeveloped as "A better way to Prague". It won't be better, but it may well be cheaper.

There is nothing cheap about Sierra Nevada Pale Ale at the Exchequer pub on Wabash Avenue in Chicago. The beer is $13.25 (£9) for a three-pint pitcher of the sort that slips down easily on a night out with the boys from the dorm; the city's youth hostel is around the corner.

As I ordered the first round, the bartender identified my accent correctly and said, "You're British, you don't tip, right?"

Au contraire, I countered on behalf of the UK, in a Gallic sort of way; in America we recognise that it is de rigueur to leave un pourboire or two on the counter for each round. But the avarice at Exchequer exceeds even the most prudent Chancellor or Northwest Airlines accountant. Due to a cash-flow crisis of Buzz-like proportions, I have taken to buying drinks with plastic. When my tab appeared at the end of the evening, the space marked "Tip Amount" was left blank. Beneath it, the pub had kindly computed the amount I was expected to leave: 25 per cent. That's not a tip – it's extortion of the kind that should have died with Al Capone. Here's a tip: drink somewhere else.