I have two different methods that I like to use. The first method I like is to bring the texture through the color of a two tone or three tone dither. I either use different textures for the different levels of light, or I just make the one texture darker or lighter using the hue saturation value node.
My second method involves setting up the BSDF shadier and the texture normally and just bringing it through one of the preset 1, 2, 3, 4, 6, or 8bit color color palette.
Which way you choose will depend on the style and look you want to go for. There are other ways too but I find that these two are the most useful for using an image texture with lighting.