StackOverflow Tags Predictor...Suggest an Machine Learning Approach please?
This exact problem was a kaggle competition sponsored by Facebook. The particular forum thread of interest for you is the one where many of the top competitors explained their methodology, this should provide you with more information than you were probably looking for: https://www.kaggle.com/c/facebook-recruiting-iii-keyword-extraction/forums/t/6650/share-your-approach 

In general, it appears that most people treated the problem as a supervised one. Their primary feature was a tf-idf, or unweighted BOW, representations of the text and they ensembled 1000s of single-tag models. Owen, the winner of the competition, noted that the title text was a more powerful feature than the content of the body of the post.