The main thing that there is to know about language acquisition among gorillas is that there really isn't any to speak of. Language seems to be one of the skills that we as humans gain access to from their enormously swolen cerebral cortex, and other physical and environmental factors which make us different than other species.
One misconception about language that makes zoologists look for traces of it in other species, whether it be in the dance of the honey bee or the echo-location of whales, is the notion that among human languages there are those that are more or less primitive. Unlike human physiology, which can be seen as a continuation from that of primates, there are no differences at all within languages that are now or ever have been spoken. All human language is vastly more complex than any that animals can be taught even with extensive training.
The most famous opportunity to determine whether a gorilla could learn human langauge is an experiment called Project Koko. In this experimental enviroment, a gorilla (Koko) that has had extensive contact with humans has learned several hundred words over the course of years. Handlers and some primate experts would argue that Koko's achievements point to the capacity of gorillas to use some human language.
Gorilas can't speak. They use many vocalizations in the wild but their articulatory system and their respiratory systems are not compatible with making complicated and varied noises. So the way they taught Koko "words" was through sign language. Some argue that Koko isn't really using langauge even when she correctly repeats signs back to the trainer. They would point out that in humans langauge is an instinct, something that gorillas don't ever do in the wild under any circumstances. And it is very difficult to distinguish these signs from elaborately conditioned behavioral reflexes, also a situation that is highly unnatural.
Another principle of language that Koko has likely not conquered is its generativity. Meaning that she doesn't innovate. Her handlers argued that she named her pet cat "All Ball." However, this could mean several things. It could be random. It could mean that she really doesn't have any mental concept of even those words even though she signs them in mainly correct environments.
In Koko's data, people will perhaps see what they want to see. Anthropomorphizing animals is very common. People say all the time that their dogs and cats understand langauge. It is usually that their handlers grow to understand them well. Many scientists would like to see primates other than humans have langauge capabilities, because otherwise langauge is a freakishly unusual accomplishment in the animal kingdom and they will have to explain it in isolation. But whatever else Koko has demonstrated, she heightens the fact that whatever she can do is vastly different both from what other gorillas OR humans do naturally.