The original name is kissing lips, and it was designed by Soon Young Lee.
Like every other origami creation you must start with a square piece of paper. I would suggest using contrasting colors so the lips don't match the mouth. (I used a red and white square paper from an old origami calender).
Step 1: With Your Square Paper You...
Fold it in half diagonally.
Then fold it to thirds. When it is in thirds it should sort of look like a house. Be sure it is symmetrical because it can affect the placing of the lips.
Step 2: Now Do This:
Fold the flap up so the point meets the upper corner. Repeat to the other side
Fold that flap down so instead of touching the upper corner it is now touching the bottom one. Repeat to the other side.
Step 3: More Steps!
Fold the flap up again, but make it so the flat part meets the half-way line made from the last step.
Fold the tips down so that even smaller triangles are formed.
Step 4: See Your Work Unfold Before Your Eyes.
Unfold it all!!! Do NOT flatten the paper; let the folds exist because you need them for the next steps.
At the top of the square there should be a really small triangle fold. Fold it down so the color is showing.
Step 5: Don't Worry It Makes Sense Eventually.
For this step use the diagonal folds. I marked them with a pencil so you can tell where it is.
Follow the folds and fold it inwards toward you. (That fold is called a rabbit ear fold)
Step 6: Less Than Half-way to Your Finished Origami!
Flip it over. Use the larger horizontal fold and fold it up/
Repeat all of the past steps to the other side. (NOT sides)
Step 7: I Can See It Now.
Fold the whole thing half.
Step 8: Almost!
Take the top and fold it down until you can see the square. If you try to fold any farther you might rip it. That is a good way to tell how far to go.
Fold that square in half so it looks like a rectangle
Sorry for the blurriness in the last photo. Anyways, fold that rectangle in half as well. There should be another rectangle shape.
Repeat all of the above steps to the other side.
Step 9: Now Let's Move It.
Make it so the flaps are facing you and they are between your fingers.
Slowly pull apart . After you are done pulling apart it should reveal the lips and mouth. to make it move just push it together and apart using the flaps.
Thanks for reading! (you must have a ton of patience)