If you mean password protected posts, you (or the administrator of the blog if it’s not you) have to give people the password. As for the person logging in with a different screen name – that’s not necessary, they should just log in with the one associated with the account they usually use.
If this doesn’t answer your question, please ask again and try to be clearer. Also would you please give a link to the blog in question, starting with http://
They will receive an email with instructions, and when they log into WordPress.com they will be able to access your blog at the level you have invited them. The screen name is whatever they chose when they signed up for WordPress.com.