Q:

How does the Google "Did you mean?" Algorithm work?

I've been developing an internal website for a portfolio management tool.  There is a lot of text data, company names etc.  I've been really impressed with some search engines ability to very quickly respond to queries with "Did you mean: xxxx".
I need to be able to intelligently take a user query and respond with not only raw search results but also with a "Did you mean?" response when there is a highly likely alternative answer etc
[I'm developing in ASP.NET (VB - don't hold it against me! )]
UPDATE:
OK, how can I mimic this without the millions of 'unpaid users'?

Generate typos for each 'known' or 'correct' term and perform lookups?
Some other more elegant method?

A:

Here's the explanation directly from the source ( almost ) 
Search 101!
at min 22:03
Worth watching!
Basically and according  to Douglas Merrill former CTO of Google it is like this:
1) You write a  ( misspelled )  word  in google 
2) You don't find what you wanted ( don't click on any results )
3) You realize you misspelled the word  so you rewrite the word in the search box.
4) You find what you want ( you click in the first links ) 
This pattern multiplied millions of times, shows what are the most common misspells and what are the most "common" corrections. 
This way Google can almost instantaneously, offer spell correction in every language.
Also this means if overnight everyone start to spell night as "nigth" google would suggest that word instead.  
EDIT
@ThomasRutter: Douglas describe it as "statistical machine learning". 
They know who correct the query, because they know which query comes from which user ( using cookies ) 
If the users perform a query, and only 10% of the users click on a result and 90% goes back and type another query ( with the corrected word ) and this time that 90% clicks on a result, then they know they have found a correction. 
They can also know if those are "related" queries of two different, because they have information of all the links they show. 
Furthermore, they are now including the context into the spell check, so they can even suggest different word depending on the context. 
See this demo of google wave ( @ 44m 06s )  that shows how the context is taken into account to automatically correct the spelling.
Here it is explained how that natural language processing works.
And finally here is an awesome demo of what can be done adding automatic machine translation ( @ 1h 12m 47s )  to the mix. 

  I've added anchors of minute and seconds to the videos to skip directly to the content, if they don't work, try reloading the page or scrolling by hand to the mark. 

A:

I found this article some time ago: How to Write a Spelling Corrector, written by Peter Norvig (Director of Research at Google Inc.).
It's an interesting read about the "spelling correction" topic. The examples are in Python but it's clear and simple to understand, and I think that the algorithm can be easily 
translated to other languages.
Below follows a short description of the algorithm.
The algorithm consists of two steps, preparation and word checking.
Step 1: Preparation - setting up the word database
Best is if you can use actual search words and their occurence.
If you don't have that a large set of text can be used instead.
Count the occurrence (popularity) of each word.
Step 2. Word checking - finding words that are similar to the one checked
Similar means that the edit distance is low (typically 0-1 or 0-2). The edit distance is the minimum number of inserts/deletes/changes/swaps needed to transform one word to another.
Choose the most popular word from the previous step and suggest it as a correction (if other than the word itself).

A:

For the theory of "did you mean" algorithm you can refer to Chapter 3 of Introduction to Information Retrieval. It is available online for free. Section 3.3 (page 52) exactly answers your question. And to specifically answer your update you only need a dictionary of words and nothing else (including millions of users).

