We went to the cinema and watched the movie. In the above situation, the speaker and listener already know what movie they are talking about.

"We went to the cinema and watched a movie." = any possible movie. It really doesn't matter which one. "We went to a cinema and watched the movie." = a particular movie, which you already mentioned. Perhaps you mentioned a book you enjoyed, and discovered there was a movie version. So this sentence makes sense, because we know which movie you mean. However, "a cinema" obviously means any possible cinema. Sorry I didn't give much attention to "the/a cinema." We native speakers will often use "the cinema" without naming it, because in most cases it is obvious to the listener/reader which cinema: the closest one, or the only one in town. I'd only use "a cinema" if I were not at home, but instead travelling through another city.

use THE to point to any specific thing, use A to indicate anything without being specific. anyway, if both are well known then best to say, we went to that cinema and watched that movie. (both the cinema hall and the movie must be named before this sentence)

As a Southern Californian who lives only an hour away from Hollywood, I don't use "cinema" but "movie theater." 1. "We went to the [local] theater and watched a movie." MEANING: General information or report about a past activity. The name of the theater was not important, because it is local and everyone knows about it. The name of the movie we saw was not important. 2. "We went to a theater [any theater] and watched the movie." MEANING: We found a theater that was showing the movie we all wanted to see. 3. "We went to the theater and watched [name of movie here]." MEANING: We went to the theater we usually go to and watched this particular movie.

a - if you have not talked about which one. The - if the person knows what you saw.