I used to do something similar, its more pop art than cartoon though.
I use a simple threshold technique.
I am assuming a basic knowledge of PS.
Open the image, copy layer, copy layer.
Switch off the top layer.
On the middle layer go to image, adjustments, threshold. (The layer will now look basic black and white)
Adjust the slider (to the left) until you have detail around the eye in the case of a portrait. OK.
Now do the same with the top layer this time keep more of the blackness, somewhere around 90/100 mark. OK.
Open a layer mask on the top layer and paint away any unwanted black detail.
When it looks ok hit Ctrl+e to merge the two layers.
Remove any stray bits of black by painting over them with white.
Create a new layer and change the blending mode to multiply.
Now paint the colours you want into this layer.
Use the erasure to get the whites.
If you need to be precise, switch the middle layer off and zoom in.
You can finish at this point.
Or you can have a play at changing the applied colours by opening a hew and saturation adjustment layer.
Pick up the magic wand tool, untick contiguous, tolerance 30ish, click on a colour and use the hue slider to change the colour.
Create new adjustment layers for each colour.
When done flatten and save.
Rhodese.
