The only official language in the Czech Republic is Czech, which is a Slavonic language like Slovak, Polish, Serbian, Russian, Croatian and Bulgarian.
Abundant usage of so-called diacritical marks is characteristic for Czech, i.e. hooks over certain letters and accents to indicate the length of vowels, which often change the meaning of whole words. Czech is spoken by roughly 96% of the population. You will also frequently hear Slovak, Polish and Romani. You can usually make yourself understood in English, German and Russian.
The deaf can make themselves understood more easily, if they use Italian or Austrian sign language, which are to a certain extent similar to Czech sign language. On the contrary, ASL or Asian sign languages are very different from Czech sign language.