Algorithms and techniques for spell checking
Here is what I built...


Step 1: Store all the words in a Trie data structure. Wiki about
trie.
Step 2: Train an RNN or RNTN to get seq2seq mapping for words and
store the model
Step 3: Retrieve top n words with  levenshtein
distance with the.  Wiki about LD with the word that you are trying to
correct.


Naive Approach: Calculating the edit distance between the query term and every dictionary term. Very expensive. 
Peter Norvig's Approach: Deriving all possible terms with an edit distance&lt;=2 from the query term, and looking them up in the dictionary. Better, but still expensive (114,324 terms for word length=9 and edit distance=2) Check this.
Faroo's Approach: Deriving deletes only with an edit distance&lt;=2 both from the query term and each dictionary term. Three orders of magnitudes faster. http://blog.faroo.com/2012/06/07...

Step 4: Based on the previous 2 or 3 or 4 words, predict the words
that are retrieved from Step 3 above. Select the number of words
depending on how much accuracy you want (Of course we want 100%
accuracy), and the processing power of the machine running the code,
you can select the number of words you wanna consider.


Check out this approach too. It's an acl paper from 2009. They call it - language independent auto correction.