In Paper Space
PAGESETUP -> MODIFY -> check box for "Display Plot Styles" in the top right for the selected layout, which should display the layout as it would print.
Depending on how you want it to look, you may need to change background color as well... SETTINGS -> select 'Drafting Tab' -> click "Colors..." and change the uniform background color for 'Sheet/Layout' or other colors in your desired color scheme.
In Model Space
Only easy way I know to accomplish this is with Layer States, however all of your entity's colors have to be set to 'ByLayer' for it to work (which can be easily done with SETBYLAYER). Right click in Layer Manager (LAYER) and at the very bottom "Save Layer States..." or "Restore Layer States..." Create a layer state for the objects with individual colors, then select all layers and change the color, create a second layer state for this "black and white" version. Switch between them with Layer States Manager (LMAN).