If you are in the western states you want to be especially careful with mouse droppings due to the risk of hantavirus. Dried mouse dung, when inhaled can cause serious illness if infected with this virus.
Avoid stirring up any dust; in other words, don't sweep, but vacuum (if you have a HEPA filter) or wipe up with a damp paper towel instead (safest). Discard the vacuum bag after you're done with the job.
After visible droppings are gone;
On hard surfaces, use a solution of 3 tablespoons household bleach and a few drops of dish liquid in a gallon of luke-warm water. Wipe down the areas where you've cleaned up droppings with a paper towel moistened with the bleach-water solution. If any dirt shows up on the paper towel, wipe again with a second moist towel. Discard the paper towel after each swipe.
If there were droppings on carpet, vacuum carefully and then test your bleach-water solution in an inconspicuous area; if no fading, spray on the affected area and "scrub" into the fibers with a clean brush or paper towel. You can also use Lysol to sanitize on your carpets and upholstery.
Clothes and washables; launder as usual with an extra hot-water or sanitizing rinse cycle, or simply launder twice.
If you want to be doubly careful, get an inexpensive black light device and shine in the areas you've cleaned; mouse and rat urine will glow under blacklight.
Life rocks when your house rolls
Senior Chief & the Cheese Queen