Image "Dracula Portrait" by Illustrator Andrew Baker
I remember the first time I played Call of Cthulhu back in College. My friends and I were D&D junkies in middle and high school from 1980 until we graduated in 1985. My high school friends never shared my deep and abiding affection for horror literature and cinema, so I was delighted to discover the Call of Cthulhu RPG.
Of course, one of the game's innovations (from my point of view, at least) was the inclusion of rules regarding character sanity. I quickly discovered that it was much easier to keep a CoC character alive than to keep them sane. Almost immediately I wrote a set of crash rules that ported the idea into 1st ed. AD&D, with some caveats.
Sanity, in that campaign, wasn't as tenuous as it was in CoC. I wrote in a loose set of rules how characters gained sanity points by level, just as they did hit points. (the Ravenloft setting offered up an even better version of this idea by assigning each class sanity points "Sanity Dice" that varied).
I set guides for experiences that cost them sanity points, and methods for recovering lost SP. Like HP, SP came back naturally with rest and quietude, (I was thinking of the notions of asylums as healing places), but they could also be restored through the use of drugs (finally a reason for characters to take dangerous drugs!) or restored through certain experiences (my initial list was a survey of experiences that I felt helped keep me grounded).
Hence, a horrifying encounter could emotionally destabilize characters, but hot meals, a comfortable bed, and therapeutic baths could all help restore that lost sanity. Since no list of restorative measure good ever be complete, characters were motivated to think of new, creative ways to quiet their minds. Watching the halfling children perform a ceremonial dance in a farming village was one of their more inspired choices.
Sanity was generally left out of the basic 5e rules. 5e did clarify what frightened meant, exactly to the person suffering the fear. It was easy enough to bring over my old 3e sanity rules into 5e. My 3e rules weren't much different than the 2nd edition rules before that. Below you will find the bare bones Fear, Horror, and Sanity rules summarized in some tables. These were brought more or less straight over from 2e, and I've been tweaking them to my current 5e campaign.
If you've never run sanity and horror rules in your campaign, you should consider adopting one of the many systems around, or devising your own. Having these rules adds storytelling opportunities and depth in ways that I'm not sure any other feature manages.