I've been looking for this answer a lot and people say diferent things are true. Is it shyer and the shyest, shier and shiest or more shy and the most shy? According to Merriam-Webster dictionary it's shyer and the shyest, shier and shiest. (http://www.merriam-webster.com/dictionary/shyer) The same goes to Dictionary.com (http://dictionary.reference.com/browse/shy). So does this mean both are right?
What Merriam-Webster is saying by including the comparatives shyer, shyest, shier and shiest is simply that these are words; it's not implying that more shy and most shy are ungrammatical. If you look at their definition of polite, it gives politer and politest and makes no mention of more polite and most polite, even though these latter forms are used quite a bit more often. (See Google Ngram.)
The same is true with shy; more shy and most shy are used fairly frequently and are not ungrammatical. Similarly, Merriam-Webster includes both the shyer and shier spellings because they are both fairly common, and neither can be said to be wrong.