Obviously, I am not a designer. So here is my programmer's easy way to get a dark-mode. I already used this method for some apps and websites before, and I (and my clients, if there were any) was always rather pleased. I am sure there are better ways out there and I am also pretty sure that designers will tell you that what I do is a bad idea.

I usually start with the light mode when creating an app. It's standard and in most cases, people are more comfortable with it. However, remember, I am not a designer. I don't care about 100% color accuracy - which is not possible on computer screens anyway. I don't care about fancy color math. That's why I prefer to use HSL colors - which is a different color space from what a computer can actually display, hence there are math errors when displaying the final color. However, HSL is a lot easier to use, because I select a hue, then set the saturation and the lightness. For a light color scheme, the lightness is usually rather high for your main colors and low for contrast colors.

Then, when it's time to create a dark theme, what I do is I try a few things. First I inverse the lightness of the colors, so I get a dark site with bright contrasts. For example, if your colors are hsl(0, 0%, 99%) for a white background, hsl(218, 99%, 65%) as your primary color and hsl(0, 0%, 3%) as your contrast / text color, then you'd switch them to hsl(0, 0%, 1%), hsl(218, 99%, 35%) and hsl(0, 0%, 97%).

This does not always work perfect, so from there, I start to shift the light factor around until my eyes don't hurt from bright elements anymore. Then, I change the saturation. Often, the saturation is too fruity for a dark theme when coming from a light theme imho. So I turn it down a bit. The result is a dark theme, using the exact same hue as the light theme, but nice and dark.

The advantage: You can keep your hue palette, which means that users will recognize the colors and the site still gives off a familiar feeling. Here's an example: