Turning this statement around will help you make sense of this. はなします doesn’t conjugate to はなす. It’s the other way around. Because はなす ends in す, it THEN conjugates to はなします which is a rule that you will learn early on in grammar studies when you get there.
The same goes for べんきょうします except a little weirder. No actual conjugation is happening for べんきょう because that’s just a single noun on it’s own. However, します comes FROM する which just means to do, which you will learn is an exception to conjugation rules. This is why べんきょう is called a “する verb,” because it’s NOT a verb until する or its conjugations are attached.
You could probably infer this from already given information, but I thought I would try to explain it in my own way like everyone does. (Great thing about forums is that it’s like having 30 teachers helping all at once.)
This page is where I learned about this and will give you more information on the subject.
http://www.guidetojapanese.org/learn/grammar/polite
I recommend this as a free grammar resource when you get to that point.
