Meeting, greeting and saying goodbye
In the Czech Republic, one of the first things you'll notice is that people say hello and goodbye to strangers in a variety of contexts. If you're from an English-speaking nation, this may take some getting used to. For instance, you should say Dobr den/Dobr veer (Hello/Good Evening) or Na schledanou (Goodbye) when you enter or leave a store, respectively.
Naturally, you don't need to introduce yourself while entering larger stores like hypermarkets, but you should definitely recognize the person behind the counter. Additionally, it is polite to introduce yourself to those seated at your table if you are dining or drinking somewhere where strangers are present. The same holds true for elevators and train cabins. And on certain regular trains, which don't typically have compartments, you'll see individuals saying farewell to each other if they've interacted in any manner, whether it was a quick chat or assistance with a suitcase, for example.
The concept behind it all is that you've acknowledged someone's presence in a small area, which, when you think about it, is rather courteous. Although it will initially seem unusual, it quickly develops into a reflex, and once you return home, you'll discover that you have to force yourself to stop doing it whenever you enter a store, elevator, etc.
When it comes to physical contact, you'll observe that Czechs often shake hands, as opposed to the more touchy-feely style of greeting and meeting that is more typical in Mediterranean nations. Handshakes are a common way to introduce yourself. It's also customary when bidding farewell.