The official Ruby on Rails API site uses the same tri-frame layout employed in the Java API site, except that the Java site's show-classes-by-package feature doesn't apply. The way to search either of these is to use your browser's "find" feature (ctrl+F). I find this setup rather irksome.
Fortunately, Vladimir Kolesnikov has brought us railsapi.com, a searchable Rails API site. It's available to use online or to download and use offline. The search returns matches by relevance and picks up on inexact matches. Below are links to the online API.
Rails version 3: http://railsapi.com/doc/rails-v3.0.3/
Rails version 2: http://railsapi.com/doc/rails-v2.3.8/