About the only way it works is when the Klingons spoke in their native language in the movies and the English translation was captioned on the screen. Can kinda add to the atmosphere hearing the different language spoken. And real time translation like in the UN can be assumed when different species speak.
I recall.one original series star trek episode, in which they seemed surprised that people spoke English on another planet they visited. Otherwise it just seems they took for granted that they could communicate with any aliens who also were almost always humanoid.