One way to experience the Czech Republic for an English speaker is to teach English there. Jobs are plentiful if not extravagantly remunerated. But for a long time it has not just been enough to turn up with a smile and native language ability. You also need some qualifications, usually a so called TEFL certificate. This usually means a month-long course which includes some theory and a lot of practice. You can take it in a variety of places (see ESL Cafe for more info) all around the world but there are several schools directly in Prague that offer the same and you get a chance to explore the city with some of your peers and establish useful contacts. I used to work for one of these schools and have seen this first hand. The school I worked for is called ITC (International TEFL Certificate) Training so I thought I'd give them a free plug here. I had a hand in designing their curriculum and training materials which are very good and I imagine have improved over time. Another advantage of going through one of the local schools is that they pretty much guarantee you a job in the city where you train (and facilitate jobs throughout the world).

Of course, speakers of other languages (particularly German) are also in high demand but the certification procedures for them are much more complicated. However, many who speak good English opt for a TEFL certificate and then adapt what they've learned for their language. Many employers accept that kind of qualification, as well.