In 2.1, the latest snapshot of staging is indexed, both full text and asset properties. For XML, you can use an XMLMetadataExtractor to ensure key elements that you need to query on within an XML document are queryable - you can find out more about this on our wiki.
For your run-time website, all content within any web project (ie, the latest snapshot in staging) is fully searchable using Search API or the Javascript API. Each web project is treated as it's own repository (in fact, each sandbox is actually it's own independent data store), and so when you are creating a web script, for example, to query the repo, you first have to set which store you are querying. Once again, documentation for this can be found on the wiki.
What does 2.1 not have? Out of the box, an interface for search isn't provided in the web client. The content is indexed underneath. The priority for the 2.1 release was to ensure search could power a run-time site and unfortunately the exposing that in our own web client was a lower priority for this release.
Adding a custom dashlet written as a web script is one possibility in the interim however. I believe there may be a community contribution for this coming in the next week or so.
KEvin