Isolate the spot where the paint splatters are by covering the area with packing tape. The products you use can damage the clear overcoat paint used on your vehicle, but this will reduce the chances of that happening. As long as you're careful, you shouldn't do any damage to the auto.
Place rubbing alcohol on all paint splatters and rub the alcohol with a clean cotton towel or cloth. The harder you rub, the more paint should come off your car. You can also try scratching at the surface of the paint with your fingernail, once it's lubricated by the alcohol.
Remove more paint splatters by applying Goo Gone. Goo Gone has an adhesive property that removes paint without leaving behind any stickiness or residue. It also has a clean, fresh scent and is easy to clean off. Apply the Goo Gone to the paint splatter, let it sit for a moment and then wipe it off.
Use a clay bar to remove any paint splatters left behind, if you have any. Clay bars are available from most dealerships, but you can also find one from some auto parts stores. The clay bar is covered in an extremely sticky substance that peels the paint splatters right off the car.
Clean off the car using soap and water to remove any traces of the products used to remove the paint splatters. Let the car air dry, or gently buff the car clean with a dry cloth. Once the car dries completely, apply a coating of wax to the surface to protect the work you just did.