I've not found how generate html format for phpDoc from PhpStorm IDE.
Or should I only use console for this this task, e.g. like this:
$ phpdoc -d|-f <PATH> -t <PATH> [parameters]
PhpStorm does not have built-in support for PHPDoc or any other doc system (ApiDoc, Doxygen etc) in terms of generating final documentation files.
PhpStorm has External Tools functionality exactly for such situations.
Or you can use any build system (e.g. Phing based on Ant / Gulp / Grunt (both require Node.js) or alike) and create such task there (PhpStorm supports all 3 of them).