False duotone:

a normal halftone printed over a flat screen of an accent color
When dinosaurs roamed the earth and letterpress was the printing process of choice, full color was a luxury few advertisers could justify.

Two color printing was the usual way to make a job stand out, and for special jobs duotones might be used for high end reproduction. This was a technically demanding process and not cheap. False duotones emerged as a way to enliven a design by mimicking the look of true duotones, while avoiding the expense.
They can still help you catch attention and make your point, even in the digital age.

Simple retro effects, step by step
The false duotone can still be useful in two color printing, where its simplicity can help you get your point across on a tight budget. It’s also a great addition to your toolbox for full color work. It can help focus attention on a point of interest, add retro style to your concept, or create a consistent look when images are pulled from different sources.
Tips and tricks
Any color or grayscale image can be a good starting point. The first step is to create a halftone, or to reduce the color range of your image to look like a halftone. The technique you use to do this has a strong effect on the final appearance.
Example 1 shows the result of the desaturate command: Image >; Adjustments >; Desaturate. This is really a process color quadtone with a neutral cast.
Example 4 shows a halftone effect created from an RGB color image by applying the Image >; Adjustments >; Black & White command. The Maximum White Preset was used to lighten highlights and midtones and create good contrast. The result was copied and pasted into the black channel of a CMYK image.
For these examples, color overlays were created with the path tool. The resulting fills were set to blend in multiply mode, with opacity reduced to 40%.
Example 2 shows how the overlays colorize the quadtone from example 1. Example 3 shows a brighter, cleaner result using the same color overlays over the simulated halftone from example 4.
For full color reproduction, you can save your false duotones as CMYK tiff images. For match color printing, set the color overlays up in spot color channels and save the file in eps format.