The official language in the Czech Republic is Czech, which is a Slavonic language (the same as Slovak, Polish, Serbian, Russian, Croatian or Bulgarian). It is sometimes possible to make yourself understood in English or Russian. German is a little less widespread.
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.