Up to date as of October 16th, 2015.
Once you have detailed language information on content, configuration, etc, which is now widely possible in Drupal 8 (see the tidbit on language assignment), you can use this data to pull out content for specific languages.
Everything is in blocks now
While not a multilingual change, it is hugely useful for multilingual use cases that everything is in blocks now. The page title, branding, breadcrumbs, menus, navigation tabs, and so on. This make it possible to customize page content much easier using the blocks controls, effectively giving site builders all the powers around page content.
Brand new in Drupal 8 are language visibility conditions for blocks provided by Language module. This combined with everything being a block allows you to swap out menus per language or localize the branding of the site.
This option is made available if you have more than one configured language on your website. While prior versions of Drupal provided visibility settings based on user roles, content types, paths, etc. this is now expanded to languages too. Here you can pick specific languages, even multiple of them (applying in an or relation).
For real advanced uses, Drupal allows you to configure a separate language negotiation method for content (on Administration » Configuration » Regional and Language » Languages » Detection and Selection). In this case the interface language of the page may be different from the content language. Block language visibility is compatible with this advanced scenario as well, allowing you to configure blocks as being "interface blocks" or "content blocks" in terms of which negotiated language will apply.
Multiple block instances
Drupal 8 also makes it possible to place the same block multiple times, which makes it possible to display it with different visibility conditions and at a different part of the page. For example, you can choose to move the contact form to the sidebar by creating a new block instance of the main page block that only applies to the /contact page and set the original main page block to not show up on the /contact page. Then you can place useful information with a map and physical address data in the main content region in a translatable block for example. The combination of these block tools with multilingual is a real powerhouse for creative site builders.
Many pages and blocks are views now
Another amazing thing in Drupal 8 is with the inclusion of Views, pages like the front page and even the content administration page became editable views. This allows you to customize what is displayed and how it is displayed and with the case of the content administration view even customize it for translation workflows or create a clone for translation workflows. And it is not just pages, several blocks also became views. The new comments, recent content, new users, etc. blocks are now views as well. This opens opportunities far and wide because Views has language filtering for content built-in (which is not new to Drupal 8), and it has rendering settings specific to language (greatly improved in Drupal 8).
Views language filtering
You can apply certain language filters or exclude specific languages here. There are also dynamic language possibilities based on the site default language or the language selected for the page. While language filtering is not new, what is exciting is the combination of almost universal language assignment as well as listings converted to Views on the frontend and backend.
This allows site builders to customize views for specific languages, apply dynamic language filtering to pages and possibly expose the language filter as needed. This also allows to easily add language specific filtering to admin interfaces combined with other features.
Views language rendering
While language filtering is acting in the views query building, you can also configure how the result is presented. When Language module is enabled and there is more than one language on the site, you can also configure the rendering language setting of views. This is configured from the bottom of the second column. The options include the language the view found the entity in (language of the view row), the original language of the entity regardless of what language views found, as well as the site default language or the current interface language (and content language if you have that configured too). Finally you can also just render in any specific language configured on the site.
In summary, Drupal 8 makes all things blocks on the page, which allows you to place multiple instances and assign page and language conditions, which makes for really powerful tools for page building. As for contents of the blocks themselves, use the built in Views module to do listings to pull data from entities with versatile language options as well. Drupal now provides a full set of tools for site builders to dynamically apply language based conditions to all parts of the website in detail.
Issues to work on
There are several issues to convert remaining special page items to blocks. Global menus at https://drupal.org/node/1869476, page elements (title, tabs, actions and messages) in https://drupal.org/node/507488, site elements (site name, slogan) in https://drupal.org/node/1053648.
You may have noticed that "Not applicable" and "Not specified" appear as options for block languages. This is silly. The interface or content language will never be one of these on a page. Picking these is useless. A specific issue for this is at https://www.drupal.org/node/2037979.
- On the previous point, the same issue that I mentioned multiple times before about which languages apply to which things would solve it on a grander scale. See https://drupal.org/node/1314250
The Views language filter for the current negotiated language is misleadingly named as far as I see. It suggests the language is based off the user's preferred language, which may or may not be true. Discuss and solve at https://www.drupal.org/node/2037979