To expand on that a bit and let you know why it works, Multiply does exactly what it says: It multiplies the value of the top layer's pixel by the value of the image's pixel and displays the result. You would expect that to give you a brighter image, but Photoshop internally converts all of the colors to a range of 0 - 1. Since white has a value of 1, multiplying a pixel by that has no effect. Black, at a value of 0, will result in 0. A value of 0.5 (127 in the color picker) cuts the value of the output by half. Thus, multiply is very good for putting things like grids and hand-drawn work into your image.

Screen works in the opposite fashion, where black changes nothing, but white makes things brighter.

Overlay is a cross between the two, where 0.5 is no change. Anything above that acts like a Screen, and anything below it acts like a Multiply.

With that knowledge, you can more easily determine which blending mode you should try based on the images you're trying to merge. Multiply to integrate line work with your image or make shadows. Screen to put in lights or glows. You can adjust the opacity of your top layer to get exactly the level of darkening or brightening you want.