The guide itself explains that generating finite levels of improbability using an electronic brain and a cup of hot tea was very well understood, but that scientists lacked the means to create a drive that could produce the infinite improbability field required to allow a ship to travel anywhere instantaneously. At the end most of them announced that the machine was virtually impossible, at which point a student reasoned that this drive therefore had to be a finite improbability. After working out exactly how improbable, he fed that value into the finite improbability generator, gave it a really hot cup of tea, and managed to generate the infinite improbability generator out of thin air. After winning the Galactic Institute's prize for extreme cleverness, he was later lynched by other scientists who had been trying to make the generator for years, who finally worked out that what they really couldn't stand was a smart-ass.
The Heart of Gold was the prototype ship for infinite improbability travel. The principle is that as its drive reaches infinite improbability, the ship passes simultaneously through every point in the universe. It is then possible to decide at which point you actually want to be at when improbatility levels decrease. Unfortunately human beings are not very well accustomed to not travelling at Normality (probability 1:1), and can be fairly distressed by events around them whilst the improbability drive is working: losing limbs, turning into penguins, planets spontaneously becoming fruitcakes, nuclear missiles metamorphosing into sperm whales and bowls of petunias, and so forth. The starship Heart of Gold was somewhat insulated against this by having an improbability-proof drive room, allowing the pilots to remain more or less normal during the flight.
It is the infinite improbability drive in The Hitchhiker's Guide to the Galaxy which saves Arthur Dent and Ford Prefect from certain death by asphyxiation in deep space after being kicked out of the Vogon ship.
The most important side effects of infinite improbability travel were that hyperspace express routes became largely obsolete, and that the History department of the university of Maximegallon finally gave up trying to figure out the universe, as completely impossible things were increasingly commonplace.
The infinite improbability drive has been superseded by the Bistromatic drive, based on the alternate math used by waiters in restaurants, which has the advantage of not having improbable side effects or improbable things going wrong.