Sorry for replying in English - perhaps you can Google Translate (I don't have RU keyboard with me at the moment).
It is most confusing description of the API, I spent many hours today trying to work out how to use it. It's impossible to decipher from API documentation.
Follow these steps:
1. Go to your Database and find "core_pfields_content" table. Note the field_X. - X will be the "magic number" for your custom field.
2. Load up Postman or Hurl.IT.
3. Change to POST, enter normal parameters.
4. For the last Parameter, enter customFields[X] where X is the number of the field from Step #1. It should look like this (see attachment).
In my example the X is 2. And the value of the custom field is "General". Registered just to post this, hopefully it will help someone.
Good luck
