The Mouth Ritual
Claimed that it would be left underneath the Dark One's sign but you'll find that it certainly isn't there. This is actually in the possession of the owner of the castle, Katrina, and is how she was able to open the mouth of the Dark One's cave at the beginning to let you out.
The Bone Ritual
Is found inside the Squid Rock, near the slippery path just outside the Dark One's Cave. It needs to be "illuminated by the light of a dead child's soul." It turns out that according to the gypsies the Will-O-Wisps who fly around the swamp at night are the souls of dead children. If you put out some candy which you can get from the general store you can scoop some up in a flask like fireflies. (you can also get free flasks from Dr. Cranium) Use the jar of Will-O-Wisps on the Squid Stone and you'll see some indentations which will let you use the Dark One's sign. Spell out the name of Avoozl, A-v-o-o-z-l, which you can learn from either the Monastery or the gypsies, and you'll unlock the Bone Ritual. Hitting the combination can be tricky, so you can hit the question mark enough times to skip the puzzle and any points, just make sure to click each of the letters until they change color and the sign is for sure pointing at them in turn, and it should open up. Make sure you let the Will-O-Wisps escape back into the swamp before morning or they'll die, and you'll lose some honor for it.
The Blood Ritual
Can be found inside the Monastery easily enough just by drinking from the keg in the basement. See the section on the town of Mordavia to learn how to get into the Monastery.
The Breath Ritual
According to the diary in the Monastery this ritual was left inside the Hangman's tree in a notch, but given that it's not there now the likely culprit was the nearby witch, Baba Yaga. The ritual is fairly simple to obtain once you've completed the main quest. See the section on Dealing with Baba Yaga for more about her quest. If you've completed the main task involving her, you can bring her an extra flask of Bone Meal or Grue Goo, or some garlic, and ask for the ritual of the Dark One.
The Senses Ritual
This one is hidden deep within the swamp next to the Mad Monk's tomb, guarded by Chernovy. Magic Users can use the Glide spell from Dr. Cranium to cross over the swamp with ease, Thieves can leap from one tuft of grass to the next with the Acrobatics skill, and Fighters can expect to slog their way through with brute force in getting through the swamp. Paladins may be able to use either the Glide spell or the brute force method. Head south until you reach the tomb, guarded by two Chernovy. Magic users can cast reversal and try engaging the monsters from a distance with spells, but they'll eventually get sick of that and cast a spell of darkness on you. Use juggling lights to dispel it, and you'll have to fight them in close quarters. Any other class can just reach the island where one of the Chernovy is and fight it directly in the usual manner. Once you've reached the tomb use the Dark One's sign on it, and you'll notice a bunch of symbols corresponding to the names of each of the rituals. You can use the question mark sign repeatedly to skip the puzzle and any points, or just enter the combination of the rituals in order, mouth, bone, blood, breath, sense, heart, and essence. As with the Bone Ritual you may need to select a symbol more than once to make sure the sign lands on it. After you're done just head north and exit the swamp for good.
The Heart Ritual
This ritual can be obtained two ways depending upon your class. Magic Users will need to complete a sidequest with the Faeries. After gaining Erana's staff they will need to head south of Erana's Garden to be frozen in place by the faeries and engage in a magical confrontation with them. Erana's staff will declare you to be its rightful owner, and the faeries will try to attack you. Quickly summon the staff and cast resistance and reversal to block direct attacks and lessen the damage from elemental area affect magic. They'll be using reversal as well, so you'll almost certainly need to use the Frost Bite spell you hopefully learned by talking to Katrina. Take out the faeries and they'll disappear and you'll obtain the heart ritual. Other classes will need to fight a wraith south, west, then south of Erana's garden. You'll want protection from the undead by amulet or spell as usual, and simply hit it with your best attacks, and you'll find the heart ritual in its lair. Paladins may also find an extra bonus or two.
The Essence Ritual
This ritual needs to be obtained within the Dark One's cave itself and is covered in the Endgame section.