Note:This tutorial will not show you how to make a real vector image, they will look like vectors but are fake, real vectors will take hours, this way is sort of a cheat, it'll only take a minute.
First of all open the image you want to turn into a fake vector in PSP (I am using version 8). i am gogin to use this image of Kelly Clarkson:
Next go to Adjust > Add/Remove Noise > Edge Preserving Smooth. Change the amount of smoothing to about 8, depending on the size of the image, it should look something like this:
Next click the sharpen tool button on the left menu its a circle thats not filled it, if you cant see it but see one of these
click the arrow next to it and then click the circle (its the one in the red box in the picture). Change the size to 500 and click on your picture, it should become clearer and look like this:
And thats it, here are some more I've made: