To learn writing a specific tone; read books that has the kind of tone you want. You can even retype a chapter or two to get a feel for how that author/tone "feels in your fingers."
Here are a few specific examples of what might work (and they are kind of in priority order as well):
- A protagonist that follows a negative character arc has the potential to leave your readers with a sense of doom and gloom (short story tip: start with the climax)
- In general dark stuff that happens and dark things that characters have to do should help get things dark - death and depression; death by sword for adventures; death by cancer for more adult dark stuff...
- A light contrast to the darkness will make things even darker, e.g. hopelessly hopeful character (that bites it)
- Descriptions and metaphors that allude to death, decay, destruction, what have you, think morbid thoughts while describing everyday things E.g. chest drawers like toothless life sucking jaws, or a bone white full moon (cliché warning), oh and night, and darkness
- Listen to depressive, dark music while writing, it might contaminate the pages
Here's an exercise: Your character's father has just hanged himself in the barn. Describe the barn from the character's point of view. Then edit the text and remove all references to the hanging. How have you described the barn?
However, I don't think you have to have so much "dark tone" in there. Just a few well chosen words here and there... or it risks turning into melodrama or exaggeration.
And, you shouldn't start with the tone, if that's what you're doing. Your first step should be to develop the characters and the plot, and write the first draft. Once you have that, see what edits you can do to turn things darker. You could develop the darker things and remove some of the lighter.