I'm not even sure what you would term as Sneakers, I'm assuming you mean Trainers.
In which case I would say that it totally depends on what they are made from, being really old school I wear Trainers with Leather uppers and my preference is for Black Reebok Classics and cleaning them involves a wipe down with a damp cloth to remove any dried on crud then wiped with a dry cloth before applying shoe polish and then buffing them with a shoe brush until shining the a quick wipe over with a clean microfibre cloth to finish them off.
The up side to this is that most places that state "No Trainers" tend not to realise they are Trainers and so I can stroll on in.