Dust the entire statue with a soft, lint-free cloth. This will remove most of the dirt on the statue and prepare it for cleaning. If you don't remove the dust first, it can scratch the statue as you clean it and make your cleaner dirty.
Dilute liquid dish soap in a bit of warm water so it is slightly sudsy.
Dip a cloth in it and wring it out so it isn't dripping.
Clean the marble with the soapy cloth. Rinse with plain water and dry thoroughly.
Mix 1/4 cup white vinegar with 1/4 cup salt to make a paste.
Smear this on the bronze with a clean cloth and buff it into the surface.
Wipe off the paste. Rinse with plain water and dry thoroughly. Any signs of tarnish will be gone and the bronze statue will shine.