I've posted a previous question similar to this in the way that it is of my WIP web-comic. The planet my friend and I have designed is strange as she wanted to create either a permanently dark planet, or a planet divided by dark and light. I'm for it as it lets me create an even more biologically diverse ecosystem (as I'm creating 85% of the alien life) though I've run into the problem of realism. As people have pointed out, and I already had a small idea of, a tidally locked planet would facilitate a dark/light surface. What I'd like to know now is if there is a way to make a credible planet with a completely dark surface that is still warm enough and well lit to cradle life, including plant life.
It is easy to have a planet with a light and dark side. If the planet is tidally locked with it's star, one side will always face the sun and the other away from it. That is easy, however, on such a planet most of the life will be on the twilight edge. Different factors would go into how far into the sun or into the 'night' you can go and still be in a livable environment.
Plants as we know them need sunlight to live, so 'plants' would not live on the dark side of the planet. However, thermal vents could provide enough heat for other life forms to survive, we have them living in the ocean deeps right now, the 'plants' would likely be more like molds and fungus, things that don't need light to survive. which also makes the life forms much more exotic.
Toward the sun will be more and more desert like until you get to a (most likely) barren sun scorched area. and farther and farther to the opposite side will be more like a polar night, cold and lifeless. The vast majority of life will crowd around the twilight area and thin out as you spread out.
On top of said tidally locked places, you could consider a theoretical alternative: A dark star. Basically a black hole, with only the radiation as a source of heat for the world. This would present a number of challenges for the species living in this planet, the most obvious one being the requirement to let the radiation of the dark star through the atmosphere.
Two rather unique challenges come to mind with this. Since the planet won't have any light worth mentioning, other senses are required to compensate. Cold-blooded to avoid detection, sonar, very light sensitive eyes, etc. As all the radiation would still need to get through and heat up the planet, we either would need an atmosphere that probably has no ozone layer to filter out UV, and perhaps even a very weak or nonexistant magnetic field. So a very ancient world that has it's core cooled down to a standstill, with a very different type of thin atmosphere to let all the radiations through. This still presents the challenge that with a less dense atmosphere, the heat would also dissipate to space a lot quicker, so perhaps the planet would still require to be tidally locked to keep even one side warm enough.
Seeing that the tidally locked phrase was added in the modified version of the question, I would first answer O.P.'s query about a planet where night and day sides are permanent.
Yes, such planets do exist and they are technically known as "tidally locked" planets. Several of these have been discovered by researchers. Take for example, the case of Bellerophon and Osiris (not the hero or god, but planets).
Now to your next problem. As you might see in detail of the above mentioned planets, tidally locked planets are most often (but not always) "Hot Jupiters". As in, they are incredibly huge planets, mostly composed of gas (instead of rocky material like earth) and they are terrifyingly close to their parent stars. On the above mentioned planets, the temperatures on the bright sides would be in thousands of degrees C (temperature of wood-fire flame is ~800 degrees). You seriously do not want to put your aliens in such a planetary hell.
But you appear to be in some luck. This article should give you some prerequisite knowledge as to where to place your tidally locked planet to make it habitable. It also discusses other aspects of a tidally locked planet that might make it suitable for life.
Plus, remember to add an ozone-like layer for protection from ultraviolet radiation. Also don't forget to add a strong magnetic field to your planet (if there's is a mention about it ever in the story of your planet) and keep it a terrestrial/rocky planet. Don't put your poor aliens on a gas giant.
You could design a rogue planet https://en.wikipedia.org/wiki/Rogue_planet Just give it an active enough core to maintain a warm enough atmosphere for life and a magnetic field