I realize I still have trouble spelling surveillance (dohled, sledování). So let’s take a closer look at that arey, maybe we’ll learn some English on the way. By the way, surveillance is a French word, but it is pronounced as if it was an English word – sɜːˈveɪləns.
Lets start with the core part: survey (průzkum): it means you collect data, usually by asking or observing. If you use a paper questionnaire (dotazník) or online form (formulář), or if you ask many people on the street, it can be called a poll (anketa). This, of course, is all voluntary (dobrovolné).
But suppose they are observing someone without their permission and knowledge – they are being inconspicuous (nenápadný). They can use CCTV cameras (closed circuit television), you can use spy camera, night-vision goggles (brýle s nočním viděním) or a bug (štěnice). If they are listening to your phone calls, your phone was tapped or wiretapped (napíchnutý telefon).
What about the people who are doing the spying? They can be called a spy (plural: spies), narks (donašeč) or snitch (práskač). If the police is listening to them in an attempt to uncover a crime or gather evidence, you might say they are wearing a wire.
If the whole state is being monitored, we are talking about state-wide surveillance, often also called “Big Brother” (after the famous 1984 novel by George Orwell). Surveillance is often connected with censorship (cenzura) and limitation of the free speech (svoboda slova).