The ritual itself is so simple it is barely worth calling a ritual in many ways.

Requirements:

Candles 4-5. Tealight candles are fine.
A mirror that you can move and position.
A room that you can completely control the lighting to make pitch black.
A cushion or chair to sit on.

Process:

Set up the seat and the mirror in such a way that you can sit relaxed while looking directly at the mirror and you can see your own reflection.

Position the candles so they do not cast light directly on your face, or are directly visible in the mirror. They can be behind you or to the side. The point is you shouldn’t be able to see the candles, only the light, and your reflection should be indirectly lit.

Light the candles, turn off all lights in the room, block light from any doors/windows/electronics. The only light should be the candles.

Sit facing the mirror and look at your reflection. Spend a few moments looking at your face. Extinguish one of the candles, and look at your reflection for a while. Extinguish another candle, and look at your reflection. You want to keep the light on your face balanced as much as possible, so don’t extinguish all the candles from one side of your body, and leave the others burning. Alternate extinguishing candles to your left and right.

The goal here is to use the minimum amount of candles to still see your reflection. It doesn’t have to be a bright or clear reflection, but you should still be able to make out the shape of your face and eyes. Once you are to that point look at the mirror again.

This is the hardest part of the ritual. Look at your face, try to look into your eyes or look between them. The hard part is for this to work you have to blink as little as possible, and not move your eyes. You do not realize how much you blink or how much you slightly shift your eyes until you’re trying not to.

As you stare at your reflection your eyes will get tired, and you’ll notice that your vision begins to blur and darken from the outside toward where you are focusing. Every time you move your eyes or blink you “reset” this process a little, so it’s important to avoid that as much as possible.

If you manage to look at your reflection in this manner long enough all your vision will fade out, so instead of looking at a mirror and your dim reflection your field of vision will be blank and dark.

While not necessary, at this point it can be helpful to try to “project” your energy or essence into the mirror. Eventually this blank vision will give away to images, most commonly reported are different faces appearing in the mirror. Otherkin often describe seeing their face as it “should” be. So elves might see another face with elven features, a therianthrope’s reflection might shift into their theriotype, otherkin who don’t know what they are but have always felt other might see something that helps them understand what they are etc.

That is all there is to this ritual. When you’re done just blink, move your eyes, and normal vision will return. You can then turn on the lights and extinguish the candle.

Obviously one should take this ritual, and the result with a grain of salt. Nonetheless it can be interesting and useful to perform this ritual, perhaps to gain insight into who and what you might be.