Prague is quickly becoming one of the most popular destinations in Europe and it's not hard to see why. The city simply oozes history, and was one of the few major cities in central Europe to escape relatively unscathed from World War II. As a result the city centre is a wonderfully preserved mix of 1000 years worth of architectural styles, ranging from Romanesque, through Gothic and Baroque, to Cubist and modernist. Prague boasts some of the most beautiful historical buildings and monuments in Europe, including the castle (apparently the world's largest and oldest, albeit much modified), the towering St Vitus' Cathedral (which took over 500 years to finish) and best known of all the stunning Charles Bridge crossing the Vlatava river. There is also a long, and often tragic, Jewish heritage.
Prague is far more than just a museum though. It is an important cultural centre; the classical composers Smetana and Dvorak were from here as was the writer Franz Kafka. Opera and classical concerts are plentiful and extremely cheap by western standards. And afterwards it is possible to get pissed out of your brain on Czech lager, probably the best beer in the world, in one of Prague's hundreds of superb pubs, which will set you back around 50p a pint.
From the UK the easiest and quickest way of getting to Prague is by air. You can do the journey by coach (Eurolines) but the journey takes well over 24 hours and costs around £70 return; by the time you take into account food and drink on the journey it's only marginally cheaper than flying. If you do want to go by coach Eurolines are usually reasonably reliable and they have what the Americans would call regular "comfort stops", but I stopped doing 24 hour coach journeys when I finished being a student. Plus coach journeys deposit you at Florenc bus station, probably the least attractive part of Prague. It is also possible to get to Prague by rail (via the Eurostar, Belgium and Germany) but as this also takes around 24 hours and will probably cost you more than a plane fare unless you are a railway fetishist or Dennis Bergkamp there's no real reason for wanting to do this.
The flight from the UK to Prague takes you over Holland and Germany and takes between 1 and a half and 2 hours.
In the last couple of years the number of airlines and flights bewteen the UK and Prague has mushroomed. EasyJet is generally the cheapest option, they fly from Stansted and Gatwick, and if you book far enough in advance the cost of a return flight starts from around £80.
Czech and British Airways are more expensive but if you book a couple of months in advance you can still get returns for less than £100 (at least you can through expedia.co.uk).With Czech Airlines you have the choice of flying to Heathrow, Gatwick, or Stansted. Czech Airlines also fly regularly to Prague from Manchester, Birmingham, Edinburgh, and Glasgow. And back again, obviously.
A cheaper alternative is BMIBaby, BMI's no-frills subsiduary, who fly to Prague from East Midlands, Manchester, Birmingham, Cardiff, and Durham Tees Valley. British European fly between Southampton and Prague.
Prague has air connections to most major cities in Europe, and you can also get to many places by train. Be warned that most of the Czech Republic's railways were laid when the country was part of the Habsburg Empire and not much has been done to them since; as a result trains are rather slow. My only experience of Czech Railways was the 8 hour journey to and from Budapest (via Brno and Bratislava); the train was very comfortable (although don't rely on getting any sleep as you'll be woken up by a procession of border guards and customs officers) and the scenery often spectacular. Local trains to other destinations within the Czech Republic may not have quite as many facilities. Remember that Prague has 3 main-line stations, so make sure you know which one you need (generally speaking most international services call at Holesovice station, north of the city centre but on the Metro system).
If travelling to Prague from anywhere outside the UK, simply take a flight to the UK and follow the advice given above. Simple