General - Races/Species in Your World
Before I dive into this section, I want to clarify: I am using the term "race" interchangeably with species. This isn't dictionary-accurate, but many games use the term "race" where "species" would likely make more sense.
I assume that whatever world/setting you are building will have inhabitants. These inhabitants may be of any number, and may take nearly any form. When creating a new race, consider the questions below. Answers to these questions might be very similar for different races in the same world, or they could be wildly different. Choose whatever makes sense to you.
What does your race look like?
A race's appearance is a great place to start, and can help inspire many of the other details.
Starting with humans as a basic template is easy and natural to do, and it works fine in a lot of settings. Star Trek and Star Wars both feature huge varieties of aliens which are essentially humans with blue skin and funny noses. Making humans shorter, broader, and harrier gets you something like a dwarf.
Starting from scratch can also work well, though it can require a bit more detail. If you want a civilized human-like society, your race probably needs some sort of prehensile appendage (hands, tentacles, etc.), a means to communicate with other members of the species, and a means to move around.
You can also take a mix of the two options. Mass Effect did a great job of this. Some races are clearly humanoid, but there are telepathic space squids, and giant quadruped dudes with gills for mouths that communicate using pheromones. There is no right or wrong answer here, so do whatever works for you.
What does your race eat?
Humans are omnivores, meaning we can eat both plants and animals. This is a huge evolutionary advantage, and may be responsible for humans evolving the frontal lobe of the brain. Despite this advantage, many humans elect highly restrictive diet such as vegetarianism or veganism, deliberately limiting their nutritional options for philosophical reasons.
What your race eats says a lot about its culture, and often shapes the race's biology. Carnivores tend to be stronger, and typically have both of their eyes facing forward to improve their depth perception, while herbivores frequently have their eyes on opposite sides of their head or on stalks for improved field of vision. Predatory races typically have sharp teeth, and frequently have claws, while herbivores typically have flat teeth. Omnivores may have any mix of these features, like humans who have forward-facing eyes and a mixture or sharp and flat teeth.
Other forms of eating might exist. Your race might eat fungus off of rocks with a long hooked tongue like a snail, or it might feed entirely by psychic energy.
How does your race acquire food?
As important as what a race eats is how it acquires what it eats. Many human societies domesticated animals and plants which were useful as sources of food and other materials. Real-world societies which developed agriculture largely ended their hunter-gatherer and nomadic lifestyles. Some societies which domesticated animals remained nomadic since their primary food source was portable and often required ranging across large areas to feed herds of hungry cattle. In either case, the ability to produce their own food allowed human societies to become considerably more dense and populous.
How your race acquires good may depend on a variety of previously-discussed factors. If your race is eats meat, they may still be hunter gatherers. If food is sufficiently abundant, the limitations of hunting wild game may not be problematic enough to prevent your race from advancing socially and technologically. If not, they might domesticate one or more animal species which they eat. If your race eats plants, your race may have taken up farming whatever food source grows well in their native habitat.
How did your race come to this world?
Your race may have evolved on your world, it may have been created by a god or some other powerful force, or it may have arrived there from somewhere else. If your race did not evolve naturally alongside the other inhabitants of the world, it may feel distinctly alien to that world. Imagine humans in a world where all land mammals evolved from the sloth.
How does your race reproduce?
Reproduction is perhaps the most important function of any species. Single-cell organisms reproduce through cell division, while mammals reproduce sexually and birth live young. Birds and reptiles lay eggs, as does the platypus for some reason. The Asari, from Mass Effect, reproduce using genetic material from another genetic parent, often including other species.
Beyond just producing offspring, reproduction has a major effect on the society of your species. Most human societies have a long-standing marriage system, which serves many purposes including guaranteeing (or at least attempting to) paternity. Lions and other species have a single male, multiple female arrangement where the alpha male reproduces with multiple mates until they are supplanted by a new alpha. Mass Effect's Salarians form reproduction contracts to guarantee suitable breeding and parentage for their children. Ants, Bees, and other hive insects have a singular queen who births all of her colony's offspring. Seahorses are all sorts of confusing, and the make gestates the children. The mechanics of reproduction can also have a significant effect on the role of gender in your society.
Your species might not follow male-female gender roles typical of many species on Earth. Warhammer 40k's Orks are asexual, and reproduce via spores, while tyranids bio-engineer their own spawn in huge spawning pools.
How long does your race live?
Modern day humans have a life expectancy somewhere in the 60's, with some living up to 128 years in extreme cases. Some species of sea life, particularly jellyfish, go through phases of life which make them functionally immortal. Most things are born, age, and die.
Some species have very distinct stages of life. Frogs hatch from eggs, then go through a tadpole phase before growing into an actual frog. Other species have less distinct life stages, and simply get larger and more functional as they grow to adulthood. Mass Effect's Asari have a maiden phase, a matron phase, and a matriarch phase, each of which involve specific notable behaviors and functions in Asari society.
Does your race have subraces?
Races in some settings have "subraces": parts of the race which may be notably different, but are still biologically similar enough to still be considered the same species. DnD has portrayed subraces in various fashions throughout its long history, including a ludicrous number of Elves.
Example 1 - Shadow of Olympus
Since I'm basing this setting on Greek mythology, Humans are a given. They're the most populous race by huge margins, and they look and behave like real-world humans. We will treat the various Greek city-states (Athens, Crete, Sparta, etc.) as sub-races, but won't make further distinctions.
I also want to include a fantasy race which makes sense, so let's look at Minotaurs. In greek mythology, Poseidon sent a white bull to a king he supported, who was planning to sacrifice said bull to Poseidon. The king then changed his mind, and decided to keep the bull. Poseidon got angry, and made the king's wife have sex with the bull, and later give birth to the Minotaur. The Minotaur was a singular monster in Greek mythology, but singular monsters are usually boring in roleplaying games, especially ones like DnD where killing monsters is a career choice. So instead let's say that the king angered Poseidon, and cursed all of his descendants to become minotaurs without the need for bestiality.
Since our minotaurs were once human, they can share a lot of human traits. They are humanoid (with a bull head), and live as long as humans. They reproduce sexually just like humans do, and even if they reproduce with humans their children are always minotaurs because of Poseidon's curse. A cultural fear of the sea also makes sense considering their origins.
Example 2 - Space Grease
Since I'm setting Space Grease in the real-world future, Humans are still the primary race. I don't think I want aliens in this setting because I really want the focus to be on the diesel-punk in space aspect.
Instead of aliens, how about robots? Modern robotics are getting pretty advanced, and throwing a synthetic human-like skin on a robot would be trivial in any realistic real-world future, but I think we're just going to toss that and have robots look very clearly robotic. They look and act human enough that they're not weird to look at, but they're a little bit weird and have stiff personalities. Because we're going for a diesel-punk feel, I'm going to say that they're fueled by space-diesel just like a car. Robots are conceptually immortal, but years of burning fossil fuels in the vacuum of space causes them to burn out in a human-like lifespan. Robots reproduce by manufacturing more robots, often from spare parts taken from other various machinery (including other robots!).
Example 3 - Heroes of Tonesvale
Since we're going for a real-world setting, most characters will be human. We can include other races on a one-off basis if characters want to play Martians or some other weird race, but we can write them as the plot calls for them, then immediately discard them when they stop being important or when we reboot the universe every few years.
They're not technically a race, but let's consider superheroes as though they were. Heroes come in all shapes and sizes, so many of the racial questions are moot. Superheroes reproduce by springing into existence by some weird event (bitten by a radioactive spider, fell from space, etc.), or by being trained by another hero or other highly skilled entity (ninjas, assassins, etc.).