I can tell you how this was shot, assuming "no special lighting equipment" is true:

• Choose to shoot on an overcast day, or cloudy (but not dim) day.
• Shoot outdoor
• Have the model look straight or slightly up, so the top of her eye reflects the sky, giving the highlight

The lips are not that shinny unless you put some lip gloss on. So I think that is a different matter (its more about choosing the right makeup than lighting the model)

If you show us some of your attempted shots, we can observe your approach and let you know what should you change to achieve the result you want.

Edit: the attempted image you post is underexposed (arguably), and the white balance is off, giving a blueish tint. The hood also makes the light uneven, a good way to counter that would be to use a reflector. Lastly to get catch light you need a light source that is bright, small, placed high and inbetween you and your model. Sometimes you can use the sky if the angle is right, sometimes you can simply use something like a -2EV flash (on camera), or the catch-light card on dedicated external flash units like the 580EXII

Edit: I edited your photo to illustrate what you can try.

Basically, you need to light your model's face EVENLY. Illustrated here is one way of doing it, using a fill flash. You can also use a reflector.

If you don't have an external flash, you can use internal flash, but the only way to control the direction of the light is to move the camera.

Finally, for even lighting, you need a lightsource of HUGE surface, that is CLOSE to the subject. In studios people use lights (softbox) as big as a dinning table to light a model's face. Basically, unless you are doing some special effects, you want soft light falling on your model's face. Bigger the light source, closing it is to the model = softer the light.

The key is to light the model with soft light across the face, showing the face in smooth shades. Not too flat, not too harsh, but smooth. Because that way the face looks three dimensional, thus is pleasing and natural.