China and Japan are the two main sources of Oriental ivory figurines --- a figurine being a cast or carved human figure such as may sit on a shelf or table for ornamentation. China has a long tradition of such carvings, going back for centuries. The Japanese first started making freestanding ivory figurines and figural groups --- called okimono --- in the 1850s, when the country opened up to trade with the West. These figurines were often carved from imported elephant ivory. Most collectors are happy to live with blemishes or stains as signs of an ivory figurine's history and character, but here are some cleaning tips that you might consider if you want to clean your figurine.
Work over the figurine gently with a soft, dry paintbrush. This is a very good way of dislodging accumulated dust from hard-to-reach areas such as the nooks and crannies in headdresses and facial features.
Wet a cotton wool bud in mineral water and apply it to the more resilient areas of dirt. Be careful to not apply pressure to fussier details such as inlaid eyes or finely carved fingers. Once you've finished, turn the cotton wool bud around and use the dry end to remove any excess moisture --- water that sinks in to the ivory can cause cracks.
Turn your attention to any heavily stained areas. If they are in a finely carved part of the figurine, you might want to work once more with a wet cotton wool bud. Otherwise, use a small segment of soft, dampened sponge. Pause and dry regularly to gauge the effect of your work --- you might, after all, decide that you don't want your ivory to look too new.