Here is the difference between a purely black & white image and a duotone image:
As you can see, the duotone image has a dual subtle color tint. The highlights are cyan, while the shadows are red. There are also tritone and quadtone images, but for now we'll stick to the simpler duotone.
There are many ways to do this, but my favorite involves working with Channels and Layers/Masks.
1. Open your Image
2. Desaturate it in your preferred way (either simply remove all color with the Sautration Adjustment, or use channel mixer).
3. Go to Image>Mode>Lab. Working in Lab allows us to separate only the lighting information.
4. Go to the Channels palette, and drag the "Lightness" channel onto the 'New Channel" icon, on the bottom. This will create a 'Lightness Copy' channel.
5. Use levels (or curves if you prefer) to increase the contrast of the Lightness Copy. It shouldn't be totally black and white, of course, but it should have increased contrast. The more the contrast, the more the duotone effect. Experiment.
6. Now you can go back to RGB color (Image>Mode>RGB)
7. Select>Load Selection and select the Lightness Copy. You will see the selection appearing.
8. Click on the New Adjustment Layer icon, and select Curves. A new Curves adjustment layer will appear, whose mask is the selection pattern.
9. Whatever you do now, you're working on the highlights. Simply select the desired color channel (e.g. Red), and adjust the curve to achieve the color you need. You will see it appearing on the highlights of the image.
10. Right click on the mask and select "Add Mask to Selection". You will notice the selection lines again. Click once again on the New Adjustment Layer (curves), and on the newly appeared mask/layer, select the mask and click CTRL+I. This will reverse the mask.
11. Now, repeat as 9. above. This time you're working on the shadows.
12. All done!