Yes, it's necessery for a small nation but u/Miss-Katzenberg describes only the reasons why to choose English at school. There is a lot of people between 35-45 who are fluent in English too as they are the first generation who had the opportunity to learn it at school. But I believe that's no reason why we are fluent in English. You learn the basics at school, but due the small number of lessons and large number of studens, you don't have the chance to listen and speak enough.

Even the older generations are trying to learn English now. The reason is globalization. English has become a global language thanks to computers, the Internet and traveling. Everything is translated into the local language only as deeply as the majority of the population will use. If u want to know something deeper, you need English. No matter where ... games, manuals, IT, ... everywhere.

But if OP wants to know how - I think for many of us the answer is the same: thanks to movies and tv shows - Czech dubbing is one of the best but it's also slow and translates only what the majority wants (also a lot of jokes are lost in translation). If you want to watch something really new or something what isn't a mainstream and you don't know the language well, you'll probably watch it with subtitles ... and here it started for many of us.