In short, the easiest way to think about the "autonomous element of deontology" (though I'm not 100% sure what you mean to refer to here) is that deontology ends up trying to respect people's autonomy. So, even if violating your autonomy (like raping you, stealing from you, murdering you, etc.) would produce greater outcomes for everyone, your autonomy is almost sacred and cannot be violated. (This is best captured in Kant's second formulation of the CI.)

As for when the formulation of the universal law comes into it, it is something like this:

You decide your duties by first thinking about what you are doing (this is what Kant calls a "maxim" of your action). So, "I am going to murder this person [because he looked at me the wrong way]!" Then, you run this maxim through the universalization test. It's kind of like an algorithmic procedure.

Then you work out what would happen if this were a universal law of nature and see if it produces a contradiction. This is where it gets hairy. There are many different interpretations on how to derive a contradiction using the universal formula, but here is a super simplification of an interpretation that I like. Imagine that murdering people whenever you felt like it is the objective moral law. Now, whenever people act on murder, people go "Yes, I should accept this, since this is what is demanded by the moral law." Now whenever you go to murder someone, they say, "Great! You are just fulfilling your moral duty, and thus it is my obligation to obey." In that case, they have just accepted/consented to your murder—at which point it is no longer murder. So, you've reached a contradiction in conceiving of your maxim as a universal law. It is impossible to murder anybody if that's the universal moral law.

This is closely tied to the "possible consent" formulation of Kant.

Notice how there were no appeals to consequences, outcomes, desirability, etc. You are literally finding contradictions in your maxims (which is "finding contradictions in your practical reasons"). I won't go too deeply into this, but part of why this is brilliant is because the normativity associated with these ethics is then tied to other forms of normativity, like epistemic normativity, rationality, etc.

The rest of the Kantian enterprise explains the source of morality, and how it is part of the noumenal world, or something, and that the CI is just kind of an algorithm that produces the "phenomenal front-end" from the insensible noumenal back-end, etc. It gets very complicated, but what is important is the kind of interpretation I have provided above.