Depending on your documents and workflow this might not work for you, but anyway ...
I'm assuming you made use of the master page for the black background, since creating a colored rectangle on the master page that fills the entire page is the easiest way to color the background of the entire document that I know. To prevent this rectangle from showing up in print, simply put it on a non-printing layer. In the layers panel, create a new layer, right-click it and select Layer options. Uncheck the option "print" layer.
Now that we've gotten rid of the black background, we need to change the font color (white on white is not very readable). The easiest way to do this is a combination of paragraph formats and object formats. First, create a paragraph style for on-screen use. Set it how you like it, presumably with white font color (in contrast to the black background that you have for on-screen usage). Now, create a second paragraph style that is based on the first paragraph style. In that paragraph style, change the font color to black.
Now, if you had to change the paragraph style of every single paragraph that would be much work, so we'll use an object style for this. For all frames that contain text, create an object style and set the default paragraph style to the first paragraph style you created. If you want to change the text color for print usage, simply open up the object style options and change the paragrah style to the style we created earlier for print usage. Note that the primary text frame is also "just a frame" that you can assign an object style to on the master page.
You could also just use one paragraph style and change the font color when you need to print your document. However, you can also quickly change drop-shadows or other relevant effects that you have applied when using the method described above. Also note that there are severeal approaches to this, including different master pages, alternate layouts, different documents or layers with reused text (using the "place and link" option) and so on ... depending on your documents and workflow you might want to approach this differently.