First of all we've to observe an Andy Warhol serigraphy.
In this kind of works we can notice 3 typical features:
1. an high contrast
2. a little square-texture
3. large zones of flat color
Then we'll try to reproduce them in our pictures.

*
I've taken my original photo (the red girl) in Flickr:
http://www.flickr.com/photos/lst1984/

I have Photoshop 7.0, but I use very common tools, so probably you can make this effect even with older versions.

*
I suggest to duplicate your image and keep always an invisible layer with the original picture.
To duplicate the image click on the Marquee tool (1) and then click, with the right button of the mouse, on your image: choose the option Duplicate layer. If you want you can give a new name to the copy (I'll call this new layer Grey).

The first step to create shadows with an high constrast is desaturating your image. Be sure that you're working on the Grey layer clicking on it (2), and then desaturate it:
press Shft+Cntrl+U
or go in Image > Adjustments > Desaturate

Now that the image is in black and white, we'll use the Curves window to create an higher contrast:
press Shft+Ctrl+M
or go in Image > Adjustments > Curves

Here try to make a curved line like the one I've done in my example. It's not important make it identical, the most important thing is that you remember to tick the Preview so you can check the result.

The level of dark and light that you choose will weigh a lot upon your final result.

To give our image a look more similar to our model, Marilyn Monroe, we'll use the Unsharp Mask:
go to Filter > Sharpen > Unsharp Mask

As usually there aren't precise parameters, but you have to use your instinct (and the Preview box) to decide the right amount and radius because every image is different; just try to don't exaggerate with the percentages or you'll get a "sandy" image.
Anyway me I used an amount of 106% and a 3 pixels radius.

Now we'll keep just the shadows of our photo, in this way:
go to Select > Color Range

Then set:
Select: Sampled Colors
and choose Selection (3) to see a little Preview of the parts you'll select (the Selection is visualized in white).

With the first Eyedropper (1) click in a dark point (2) of your image.

Personally I always use a Fuzziness that allowed me to see in white (I'm mean in the Preview) at least eyes and nose.

Create now a new layer (I'll call it Shadows) clicking New layer in the Layers window (1).

In this new transparent layer we'll have the shadows:
use the Paint Bucket tool with a black color and click into the area previously selected with the Color Range Selection.
If you set the other layers as invisible clicking on the eye (2) you'll see better the result.

Return working on the Original Picture layer:
with the Pen tool (or with your favourite tool) select the face and the other parts of the photo where the skin is visible.

Remember that you have not to follow perfectly the edges, like in Andy Warhol's serigraphies.

If you use the Pen tool, when you have finished to draw the path, click with the right button on your image and select Make Selection:
in the window set the Feather Radius to 0, tick the Anti-aliased option and create a New Selection.

Create a new layer, like in the 6th step, and fill the selection with the Paint Bucket tool setted on a pale pink color.

Now repeat the steps 7 and 8 for any part you want having its own different color.
I suggest you to create a layer for every part, so in case you'd change idea on some color it'll be easier change it.

Personally I've done a layer for the hair, the backgroung, the skin, the eyeshadow and one for mouth, teeth and eyes together. When I've been sure of the result I've merged all the colored layers (Ctrl+E).

Now we just need to add the little square-pattern, and we'll procede in this way:
1. create a new layer, all white (you can fill it with the Painter Bucket tool or simply color it with a big white Brush)
2. go to Filter > Sketch > Halftone Pattern

For the size and the contrast choose 1, and a Dot Pattern type (1). Be sure that your Foreground and Background colors (2) are setted on black and white.

Lastly, to give our pattern an old look:
go to Filter > Noise > Add noise

In the window choose Gaussian Distribuition (1), and tick the Monocromatic option (1). I suggest an amount of 10-20% in this case, but it's always better checking the result with the Preview.

The Pattern layer has to be setted in a Multiply style (2) and filled for a 20-25% (3).

Now that the tutorial is finished, just a last precisation:

Obviously changing the colors your work will have a different look, but even steps 3 and 5 are very important because changing the values your results could be very different.

If you want you can even delete the background, to make the image less confused and concentrate all the attention on the subject.

*
I hope my tutorial could be useful, and I ask you to be merciful if my english isn't perfect.
Grazie (thank you).