How do I replicate the legacy "Current Search" block functionality after upgrading to 7.x-1.0-rc1?

After upgrading to Facet API 7.x-1.0-rc1, you will need to enable the Current Search Blocks sub-module that is now bundled with Facet API. After enabling the module, a default configuration will be provided that adds a new block titled "Current search: Standard". After adding that block in the appropriate region, it has to be configured so that is is active on the searcher, or search page, of your choice. See the images below for details:

If you have multiple searchers that require "Current Search" blocks, the "standard" configuration will have to be cloned at admin/config/search/current_search to create more blocks. Each block can then be associated with the appropriate searcher via their respective block configuration page.