Star Trek: Know your Aliens
You already know what humans are, but it's important to know that in the Star Trek world, Earth is part of what's called the "United Federation of Planets" (usually "the Federation," for short) which is a centralized governing body consisting multiple alien races, hundreds of planets, and thousands of colonies. The "capital" of the Federation is located on Earth.
The Federation's military arm is called Starfleet. Star Trek (Classic) and the three television series that follow it are about the lives of people who serve Starfleet as the crew of various starships and space stations.
Vulcans look pretty much like humans, except they have pointy ears and eyebrows which angle up more than human eyebrows. I'm also under the impression that most of them have dark hair cut very short, although searches on Memory Alpha return evidence of a number of different hairstyles.
Vulcans value logic and reason above all else, and try to avoid being biased or influenced by emotion. This contrasts sharply with the humans around them, who tend to be much more motivated by emotion. All the same, Vulcans and humans seem to get along pretty well. Both species are also prominent within the Federation, and Vulcans appear as main characters in three of the five Star Trek TV series.
Klingons originally looked much like humans, but with very bronzed skin, upswept eyebrows, and Fu Manchu-esque facial hair. The Klingons are not members of the Federation and are shown as having very few redeeming qualities. The Klingon Empire stands as the main antagonist of the Federation in the way that the Soviet Union was the antagonist of the United States at that time.
For the release of Star Trek: The Motion Picture, the look of the Klingons was radically redesigned. The Klingon forehead now had very prominent ridges running down to the bridge of their nose, almost like an exoskeleton, and they dressed in complicated metal uniforms which were inspired by Feudal Japanese armor. They also got their own language (full of harsh-sounding consonants) and their own alphabet (full of menacing, dagger-like shapes) with which to write it.
Tribbles are actually animals, not a sentient species, but no discussion of Star Trek creatures would be complete without them. They're basically just balls of fluff, about the size of a softball or a bit larger. They make an attractive purring sound when you pet them, so they're very attractive pets. Unfortunately, they breed like crazy and can consume all of the food on a planet or in a ship if not kept in check. (Also, they hate Klingons and emit a high pitched screeching sound when Klingons are around, instead of their usual purring. The antipathy is mutual.)