[noun] + を + なさる [noun (する verb)] + なさる ご + [noun (する verb)] + なさる
なさる is the honorific (尊敬語) form of する. You use it for what someone you respect does – a teacher, a customer, your boss – and never for yourself. It replaces する on its own, or at the end of a する-verb: さんぽ散歩なさる, ごよやく予約なさる.
For your own actions, the humble partner is いたす.
なさる is a godan verb with an irregular ます-form, なさいます, and an irregular imperative, なさい. Everything else is regular: なさった, なさらない, なさって.
なさる only covers する. Other verbs become honorific with お〜~になる: おかえりになるお帰りになる, およみになるお読みになる. Mixing the two is a common mistake.
A Sino-Japanese する-verb can take either: ごよやく予約なさる or ごよやく予約になる.
The imperative なさい is used on its own as a command to children and students, and carries no respect at all; it has its own entry.