how to form hydrogen ion and hydroxonium ion from hydrogen trioxonitrate [v] using formula
Did you finish your question? What comes after "formula"?
I assume you mean HNO3 but you should call it nitric acid. Hydrogen trioxonitrate(v) is not an IUPAC name for nitric acid.
HNO3 + H2O ==> [H3O]^+ + [NO3]^- produces the hydronium ion (hydroxonium ion). Technically I don't know how you would produce a free hydrogen ion because in water solution the free hydrogen ion doesn't exist. Perhaps finishing the question would help.