Mouths are a great way to show the mood a character you are drawing.
This quick tutorial illustrates how to draw different anime and manga mouth expressions from the front view.
Anime and manga mouths are highly simplified. The lips are usually not drawn at all and the entire mouth can often be drawn with just one or two lines. They also tend to be drawn smaller than normal mouths but depending on a characters expression they can also be drawn much larger than normal. This is especially true if the character is very emotional (angry or happy).
If you do want to draw lips on an anime style mouth you can check:
For drawing anime mouths from the side see:
Placing Anime and Manga Mouths on the Head
to place the mouth on the head you can draw two horizontal lines one under the chin and one under the nose. The bottom lip will be located in the middle between the two. The mouth opening will be just above that. Since often in anime lips are not drawn at all you can always just draw the mouth opening slightly above the middle of the nose and bottom of the chin area.
If the mouth is open or the lips are moved from the normal state you can adjust the size and position accordingly.
Drawing Anime & Manga Mouths Step by Step
For an open anime mouth start by drawing the outline of the mouth first. Then fill in the details (usually just tongue and/or teeth).
When shading or colouring the inside of the mouth should be the darkest with the tongue slightly lighter and the teeth the lightest (usually just white).
Closed Anime & Manga Mouths vs Open
When drawing the characters head draw the jaw lower for a mouth that is open and higher for one that is closed.
Finally here is a finished drawing of the head so that you can see what the mouth will look like with the other parts of the face included.