Settings → Appearance. Two choices: a palette — Core Ocean, Teal Mist, Forest Calm, Sunset or Midnight — and whether it is Light, Dark or Match my device. Both apply straight away; there is nothing to save.
It is per device, not per account
The choice is remembered on the machine you are using. Your phone can be dark while your laptop is light, because that is a fact about the screen in front of you rather than about you. It also means a browser that is not keeping site data — a private window, for instance — will start from Match my device each time.
What it does not change
It covers the site around the pages: the nav, your feed, the composer, Settings. It does not repaint anybody’s profile, including your own.
A profile is shown in the colors its owner chose, to everybody. Reading in dark mode and opening a light profile shows you that page light, inside dark chrome. Forcing your setting onto somebody’s page would repaint the thing they made, which is the opposite of what this place is for.
Your own page’s colors are under Page design.