How can I predict the post popularity of reddit.com with hidden markov model(HMM)?

An HMM doesn't really make sense (echoing what Dries said). If you want to use an HMM, you would have to justify it by asking "Can Reddit posts be represented by a Markov process?" I can't think of a way to make that sentence true and still take advantage of the features related to a popular post.

Consider the possible feature set: the time it was posted, the user posting it, the type of post (link / image / text), the subreddit, the number of subscribers to that subreddit, a score of positivity / negativity, number of words in the title etc. Don't count out these features.

I don't think it makes a lot of sense to use HMM's for this problem. What I would suggest is some kind of text-based classifier. If you want to use a cool technique, you could use a neural network to learn based on the text of successful posts.

On the other hand, If you want to use an easy technique you could make a predictor for the popularity such as a regression model (try to predict upvotes).