Some kinds of plums are good eaten fresh but the Oriental plum is green and much too sour. If it is the kind that is much too sour to eat then maybe it will work but I am not sure. It is very acidic. You want to pick them before they start to turn yellow and loose their acidity. Here in Japan they are picked at the beginning of the rainy season, or early June.

You need a big, clean bucket with a loose lid and a large, heavy stone.
Pick and gather together the unblemished plums and remove the calyx's. Soak them in a bucket of water overnight. Take them out of the water and, what I do, is get a little cup of awamori or shochu and dip each plum into the alcohol, as a disinfectant, and return them to the bucket. Add lots of salt and mix them all about. Last year, with about 60-80 plums, I used a large handful of salt(I have big hands). If you don't use enough salt you risk mold and too much is just really, really salty but I guess you are better off with more than not. I have heard about 10% is common.

Put the heavy stone on the them and cover. Store in a dark, cool place! A flat pressing lid, a clean round board, or something, with holes in it and about the diameter of the inside of your bucket is good to put the heavy stone on and evenly distributes the weight.
It takes about 6-8 weeks but after about 3-4 weeks I gather a whole bunch of red shiso(perilla) and mix salt in with the leaves in a large, open bowl, squeezing and mixing, squeezing and mixing in the salt and then adding these leaves amongst the plums. Replace the heavy stone and wait until the end of July or beginning of August when the weather is forcast for no rain. Take out the plums and dry for 3 days or so depending on the kind of weather. Put them in jars and age for at least a half year but it can be hard to wait!!!! They best are aged for years and people often can accumulate umeboshi over each year so as to keep batches stored for 5-10-15 years or more!

After the final 3 day drying I like to put mine back into the brine, for a dip, before storing them in jars. I like my umeboshi to be a bit on the wet side rather than dryish. The left over brine, umeboshi vinegar, should be kept for using in salad dressings or is an excellant remedy for soar throats by gargling the salty, potent stuff.