I understand it should be
How does it compare
because the do has stole the s, but what is the reasoning behind it? I don't want to make the same mistake twice, so I feel I need to understand the reasoning.
Because, as with can or should, do is a modal verb, and as such it is always followed by a verb in its basic form: basic form being the verb without the introducing to.
Compare can be transitive or intransitive.
Transitive, identifying differences:
Intransitive, be comparable