Plone has a beautiful search box with a "Google suggest" like functionality for its site. It even indexes uploaded documents like PDFs. Does anyone know of a module that can provide this kind of functionality in a Django site?
Plone implements it's LiveSearch feature by maintaining a separate metadata table of indexed attributes (fields such as last modified, creator, title are copied from the content objects into this table). Content objects then send ObjectAdded/ObjectModified/ObjectRemoved events, and an event subscriber listens for these events and is responsible for updating the metadata table (in Django events are named signals). Then there is a Browser View exposed at a fixed URL that searches the metadata and returns the appropriate LiveSearch HTML, and finally each HTML page is sent the appropriate JavaScript to handle the autocomplete AJAX functionality to query this view and slot the resulting HTML results into the DOM.
If you want your LiveSearch to query multiple Models/Content Types, you are likely going to need to send your own events and have a subscriber handle them appropriately. This isn't necessary for a smaller data sets or lower traffic sites, where the performance penalty for doing multiple queries for a single search isn't a concern (or you only want to search a single content type) and you can just do several queries from your View.
As for the JavaScript side, you can roll-your-own or use an existing JavaScript library. This is usually called autocomplete in the JS library. There is YUI autocomplete and Scriptaculous autocomplete for starters, and likely lots more JavaScript autocomplete implementations out there. Plone uses KSS for it's JavaScript library, the KSS livesearch plugin is a good place to start if looking for example code to pluck from.
http://pypi.python.org/pypi/kss.plugin.livesearch
And a tutorial on using KSS with Django:
http://kssproject.org/docs/tutorial/kss-in-django-with-kss-django-application
KSS is quite nice since it cleanly separates behaviour from content on the client side (without needing to write JavaScript), but Scriptaculous is conceptually a little simpler and has somewhat better documentation (http://github.com/madrobby/scriptaculous/wikis/ajax-autocompleter).