Yeah, I use PSP too.
What I know is that screen works like the opposite of multiply: it multiplies the inverse of the current layer with the inverse of the underlying layers, then inverts them all back again. (In mathematical terms: if multiply does x = a * b, then screen does x = 1 - (1-a) * (1-b) )
If that makes no sense, just think of screen as a version of multiply that makes things brighter instead of darker. Screening with black gives the colour you paint with, screening with white gives white.
I tried it out just to see what the result was: