Integrating Search API and Views?
The important points, which I can't seem to find stated clearly anywhere:


Each Search API search index you create becomes an option in the "Show [content]" dropdown at the top when you first create a new view. Unlike regular search views (where you could just take any old view and add a "Search" contextual filter), to use search API in views, you have to create a special type of view, choosing and fixing the search index to use at the point of creating the view, by choosing it in this dropdown. 
You'll need to pipe the actual search terms in somehow. A common way is to use the "Search fulltext" contextual filter, which interprets an argument in the URL as the search terms to use. There's also (depending on search server, I believe) the popular "Search More like this" option, which uses the content of the entity loaded via the contextual filter as the search terms (so if it's a block on a node page set to use the node's nid, it gives you results as if you searched using that node's content). Another way is using an exposed filter then getting the search terms from the input or exposed filter part of the URL query string.
For reasons I don't quite understand (probably something to to do with how entity API module does views integration for entity views, which has some limitations, more info at http://drupal.org/node/1378656), some elements of a Search API view are different to how they would be normally. For example, where in a node view, the path would be [path], in a Search API index view on a search index set to search nodes, it's [url]. It's no big deal, mostly the differences are fairly easy to figure out, but it's something to watch out for. Some things e.g. some relationships don't work for similar reasons - test complex views thoroughly and look at both Search API and Entity API issue queues if you find problems.


There is, technically, a documentation page that touches on some of this, which might be of some use to someone.