On an expedition to an inhabited planet, we encounter intelligent life. However, they are not as intelligent as we are. They have language, but it's less expressive and more concerned with the immediate - a strong vocabulary and simple grammar relating to hunting or foraging, say, but no deep abstract concepts yet.
I want to avoid just simplifying English. For instance, the "me-tarzan, you-jane" type language where most of the "primitiveness" comes from forgetting words. I want to make it sound like an actual language, in other words. In addition, I want to make it so that what it can express it can express naturally and fully. I go back to hunting, foraging, perhaps speaking about the immediate natural environment. Such a species would clearly be able to plan a hunt, for example, and would likely have a rich language for doing so.
What should I consider when making this up to achieve my goals?
EDIT: although there are many great answers, I think I should further specify to give more context. I'm not thinking of human-like hunter-gatherers. For instance, if we were to travel to the past, say, 50,000 years ago, and take a baby from that time and transplant them here, that baby would be able to learn our language and would not know that she is different in any way (time paradoxes aside). On the other hand, we can't do this with a chimp baby, although it is remarkable what we can do with chimps. I'm thinking somewhere between ape and human.
For instance, the language might only have one word for "danger" (why not? I don't need you to know what to run away from, just that you should run away) but I might have many words for "hunt" (depending on what I want to hunt, how I want to hunt it etc). Other than that, though, I'm sort of stumped as to what such a language would sound like.
EDIT 2: For the curious, I've done a bit of research and it seems that the most important feature of human language (compared to animal communication) is "displacement" - the ability to communicate about things that are not present, either in space or in time. I believe that, as a minimum, my creatures would need to be able to name a place and name a thing, so that, for example, the sentence "get berries at the hill" could be communicated, perhaps as simply as "berries hill". (Obviously this is in English to make this edit easier to write and understand). We could inflect the words to indicate meaning. For instance, "berries hill^" (raise last syllable, like asking a question) could indicate "we need to go get berries at the hill" while "^berries hill" could indicate actually asking a question (are there berries at the hill yet?)
a LOT more thought needs to go into this, obviously.
EDIT 3: I took a stab at outlining the language here: What are the limitations/expressive powers of my constructed proto-human like language?