Cold moist stratification of the 'cleaned' seeds (in the fridge, in a ziploc bag with some moist peat) over winter, then plant in spring. Expect a high germination %

Be aware that persimmons are dioecious - there's a 50-50 chance of any resulting seedling being a fruiting female OR a non-fruiting male... and no way to know which you've got until you grow them through their juvenile period, which may take 10 years or more. And... if it is a female, the fruit quality/size may or may not be comparable to that of YOUR persimmon.

Or, you could grow it out for a year or two, use it as a rootstock and graft or bud on a scion from your persimmon, creating a clone of your tree.

Depends upon what kind ofpersimmon you have. Asian or American.

See this for Asian persimmons, via seed, cutting, or grafting:

http://fruitandnuteducation.ucdavis.edu/fruitnutproduction/Persimmon/Persimmon_Propagation/