Copies of the brief are sent to the opposing side, who then has a specified number of days to file a responsive brief.
Copies [in NY] are served on the Clerk of the appropriate Appellate Court, in a format and number of copies required by Court rules, and on opposing counsel. Respondent should contact their attorney for a copy, or go to the Clerk's Office, if allowed, and either read, or pay for a copy [Once filed the brief is a public record].