Remove the lampshade from the lamp base.
Blot as much of the paint as possible with a dry paper towel. Do not wipe it because that will only spread the splattered paint on more of the shade's fabric. If the paint has started drying around its edges, try to scratch it off with a fingernail.
Wet a paper towel. Wring it out so it is not dripping wet. Set the paper towel directly on the latex paint, and allow the water to penetrate the lampshade fabric for one or two minutes. Do not rub the paint.
Pour 1/4 cup dish-washing soap and 1/4 cup cool water in a spray bottle. Shake the mixture, and spray it over the paint. Blot the paint with a sponge. Rinse the soapy water off the lampshade.
Repeat Step 4 until the paint is no longer visible or no more paint comes off the shade.