Traditional or "Missionary Cunnilingus"
The woman lies on her back and opens her legs. Her partner kneels between her legs, spreads open her folds and licks her clitoris and vulva. This is the standard position for cunnilingus and allows for easy access to the clit, as well as the ability to insert fingers or vibrators into the vagina.
This time the woman sits in a chair or on a table and opens her legs. She may recline back a little onto her elbows for support. Her partner is still in essentially the same position between her legs.
Face Sitting or Squatting
The woman's partner lies on the bed and the woman straddles his face. She can do this either by kneeling with one leg on either side of his/her head, or by squatting over his face. The latter can be harder on the leg muscles but gives the woman more control over where her partner is licking. Face sitting can also involve licking the anus, and in female domination scenarios, can also involve actual sitting, resulting mild consensual smothering of the man.
Reverse Face Sitting or The "68" - This time the woman faces away from her partner who is lying flat on the bed. This position is better for anulingus and vaginal stimulation. Usually the clit will need to be manually stimulated
This is similar to the traditional cunnilingus position except the woman puts her legs in the air, or on her partner's shoulders. The idea here is to make the woman's vulva and anus more accessable to her partner's tongue. Pillows placed under her lower back and hips will help to angle her groin towards his face.
As the name suggests, the woman kneels on all fours as she would during doggy style sex. In this case her partner can do one of two things. He can kneel behind her and push his face into her rear end. This results in a more expansive lick and allows for extensive anulingus and tongue-fucking. Alternately, he can lie back between her legs facing upward and lick from there. He may need pillows to help him gain height, or else the woman can open her legs a little wider to bring her cunt to his face.
Yes, it's just like the yoga position. The woman lies on her back and swings her legs all the way over her head so her ass and cunt are facing the ceiling, or thereabouts anyway. Her partner can then approach from two directions to lick her clit and cunt. Obviously this position requires some flexibility and it can be difficult for the woman to hold for long periods of time. Even so, it does help blood to rush to the head, which can result in strong orgasms.
Some women like to close their legs when they orgasm, which means that this position is best for cunnilingus. It's also rather difficult for the man, but not impossible. The woman lies on her back as with the traditional position, but she keeps her legs closed. Her partner must straddle her knees and use his fingers to pull her labia apart to reveal her clit. He then licks until she comes.