I made this guide for PSP 8.0 but it will probably work in any decent graphics program. I'm assuming you have some basic knowledge of the software, creating new images, gradients et cetera.

1. Create a picture with the size of the backdrop you wish to have, and fill it with a black and white gradient.

2. Reduce color depth to 2 colors. In PSP this is done by choosing Image > Reduce Color Depth > 2 Colors (1 bit)

You may be asked if you want to flatten the picture to a single layer, chose Yes.

A new window will open with these options:

Image

Select Ordered Dithered as I have done here. If you wish you can experiment with the other dithering types available, but for the classic look chose Ordered Dithering.

3. Now you have a nice dithered gradient, but perhaps you want other colors than black and white? Changing them is easy, just Select Image > Palette > Edit Palette...

Now you will see this window:

Image

Double click on the color you wish to change, another window will open where you can set colors just like you do when you choose paintbrush color.

Now you're done, just save the image and insert it in your game.