My subjective impression is that "the question of how to do X" sounds more natural than "the question as to how to do X." An Ngram chart of the phrases "question of how" (blue line) and "question as to how" (red line) for the years 1800 through 2007 suggests that this was not always the case, but that during the twentieth century popular usage gravitated strongly toward the former:
I didn't include the phrase "question how" in this first chart because it would introduce many matches that weren't structured similarly to the other two phrases of interest. However adding definite articles to the three phrases yields an interesting chart for "the question of how" (blue line), "the question as to how" (red line), and "the question how" (green line):
I don't see any syntactical reason to prefer one form over the other two; but the preference in published writing for "the question of how to do X" seems to be meaningfully large and therefore may be a legitimate consideration if you are trying to use the most common form of the expression.
One further option arises from the fact that constructions of the form "the question how to do X" are often framed as actual questions embedded in the larger sentence, by adding a comma after the word question, altering the included verb as needed, and adding a question mark at the end of the sentence, as indicated here:
This thesis addresses the question, how does one do X?
This thesis addresses the question, How does one do X?
In such instances, the decision about whether to capitalize how is a matter of stylistic preference.
I believe that the same general analysis would apply to expressions of the form "the question of whether X is true."