Traditionally, Anime/Manga characters are portrayed as "lipless". However, it is possible to have characters with full, even pouty, lips. The trick is to draw the mouth in the traditional anime way then apply the lips to it. If you keep the proportions right it will look good...I'll show you.

Understand the Shape

The mouth has a "Bow" shape to it. The upper lip is like those seagulls you used to draw when you were a kid. The lower lip is more like a Bow from a bow and arrow set.

Open and shut case

These shape principles remain the whether the moust is open or shut. However, The wider open the mouth..the more streched the lip therefore you should draw it thinner if it is WIDE open.

Step 1: The setup

Now that you now the difference between the top and bottom lip we can begin to apply that to our traditiona anime mouth.

Here's a low detail anime mouth. If there was an upper row of teeth visible and maybe a small shadow to define the lower lip we would be done...but we are going to expand on this.

Step 2: bow in the top lip a bit

Start to work in that Seagull shape to the top lip. Begin to visualize this as a 3D object. I have made a few centerlines here to help me define the correct angle of the lips for the next step.

Detailing

Work in the lips as shown here and in the first 2 pics. Add some teeth and darken the interior of the mouth (if visible) to give it some depth.

If you are coloring the piece..it's best define the lips through color shading. Upper lip should be darker than the lower lip.

Keeping it "Anime"

Traditionally, if a person is looking straight ahead you could draw a dotted line from the middle of their eye down their face and find the corners of the mouth. That's how you would normally determine width. BUT, since this is anime, Mouths are only as wide as the inside corner of the eyes (for women).

I intentionally drew this pic in "Ultra-Shirow" mode since Shirow is one of the few manga artist that actually draw lips.

Check out Adam Warren's stuff too. He tends to draw lips on his characters as well ..a little too big sometimes but it still looks good.