For the purposes of this discussion, duotone refers to monotones, tritones, and quadtones as well as duotones.
Duotones increase the tonal range of a grayscale image. Although a grayscale reproduction can display up to 256 levels of gray, a printing press can reproduce only about 50 levels of gray per ink. For this reason, a grayscale image printed with only black ink can look significantly coarser than the same image printed with two, three, or four inks, each individual ink reproducing up to 50 levels of gray.
Duotones are printed using a coloured ink for the highlight colour. This technique produces an image with a slight tint and significantly increases the dynamic range of the image. Duotones are ideal for two‑colour print jobs with a spot colour (such as a PANTONE Colour) used for accent.
Because duotones use different colour inks to reproduce different gray levels, they are treated in Photoshop as single-channel, 8‑bit, grayscale images. In Duotone mode, you do not have direct access to the individual image channels (as in RGB, CMYK, and Lab modes). Instead, you manipulate the channels through the curves in the Duotone Options dialog box.
Check the Duotones on press—don’t leave it up to the printer to interpret what you are trying to achieve with your Duotones. You really do need to be on press.
If you have prepared the file for the black plate to print shadows and gray ink for midtones and highlights, you have a great deal of flexibility to vary the ink on press to achieve the look and feel you like. Most of the adjustments made will likely be in the black ink, which can also affect your type on the page. (Ideally you would have a second black unrelated to type for your Duotone.)
Reduce black for a grayer reproduction, and increase it for denser shadows. Depending on the steepness of the contrast curve used on the black printer, either your black inks will creep into the midtone and darken your overall reproduction or it will only affect shadows.
Be careful of varnishes on your image, as they can yellow over time and change the image color.