China

Washing

Washing the piece in warm water and a good washing-up-liquid may be sufficient. If it is made of metal or wood as well as china, don't immerse it in water but wipe the china parts with a cloth wrung out in warm water and detergent, and 'rinse' them with a clothwrung out in warm water alone.
The dirt may be rather stubborn so you may need to scrub gently along the cracks with an old toothbrush, using neat  washing-up liquid. You can use a scouring pad - Brillo, for instance - in really bad cases, but take care not to scrub off any unglazed decoration.
Be careful not to make matters worse when cleaning china. If you immerse it in very hot water you may well cause more of the hairline cracks you are trying to disguise. It is worth testing  a sample area first, where the damage is least likely to be seen, by wiping it over with a cloth wrung out in very hot water. If washing fails try 'Stainfree' tablets, available from chemists and hardware stores. These dissolve in hot water and make an effective solution which deals with most stains in about an hour. Try a second time if the first treatment doesn't seem sufficiently effective.   

China

Cleaning

Some junk china may need no more than a good clean to make it usable again. A shiny glaze is almost always painted on to a finished piece of china before it is fired. This may develop hairline cracks (probably through being overheated) in which the dirt of many years accumulates, emphasising the cracks and making the piece look far more disreputable than it really is. Usually these hairline cracks seem to 'disappear' completely when cleaned.