In Photoshop, how do I take an image in shades of gray, and transform it into shades of whatever color I want? I don't know the term for it, if there's one, neither the property of the image I would be changing with this effect, but I think it's easy to understand.
Make sure you're working with a Grayscale image and then go
Image > Mode > Duotone, you'll bring up this dialog:
From there choose the colors you want to use by clicking on the color block. Adjust the mapping of gray to color by clicking on the curves (the block with the diagonal in it).
You can achieve different effects by adding multiple colors. For example, this image:
With this tritone:
Produces this image:
Gradient Map Adjustment Layers are awesome, precise and exactly what you're after.
Gradient Maps map the underlying image's brightness to a point on the gradient. This means you can choose exact colours for highlights, midtones and shadows.
There's a bit more info here: https://graphicdesign.stackexchange.com/a/10789/3901