This was a black and white image that I inverted in Photoshop with command/control+i.
I want to convert everything that is black to a color. How would I replace the black with a different color?
There is a very simple way to do this in Photoshop. Because you've inverted the image you can now use the Screen Blending mode and this will knockout the black in your layer. Underneath your layer you would implement whatever color background you like to replace with the black.
This works because the Screen Blending mode essentially acts as an inversion of the Multiply Blending mode-- which means of course when you invert your image you would have to apply the inverse of Multiply to knockout the black.
Another way to do this is by using a Gradient Map on top of your layer.
Then select the 2 colours you want (ex. Red and White).
There are also plenty of other methods to do so, but I think this and AdamSchuld's method are probably the simplest.
Window -> Channels, command-click the
RGB layer and then make a new layer from selection. Now you don't have a background anymore and you can simply put another layer behind it as its acting background.
In the future I'd suggest some creative Googling because this is a rather common question (that's even been answered before on this very website).