How do you make an oral motion outside of a hearing?
Best practices would usually be to respond to the motion in writing before the hearing, both procedurally and on the merits, because judges now and then ignore procedural errors by a party and if you haven't responded you will be left flat footed at court if the judge ignores your procedural objection.
Of course, if you are really sure that the motion will be dismissed upon your objection on procedural grounds (and the fact that you are posting on this board suggests that this is probably not true), and the matter is very time sensitive (i.e. there wouldn't be time to refile the motion at or after the hearing because it would be moot by then), not tipping off the other side in a way that would allow the other side to correct their mistake would probably be a better strategy.
Ultimately, however, you have not provided enough information about which court system this is in and what kind of case is involved to provide a more specific answer. As the tags to your question indicate, these are questions of civil procedure and court rules. Those rules differ from court to court.
For example, the way motions are handled, even within the City and County of Denver, in Colorado, where I have my law office, differs materially between the limited jurisdiction Denver County Court, the general jurisdiction Denver District Court (which is quite similar to the U.S. District Court procedurally), the Denver Probate Court, the U.S. Bankruptcy Court, the Colorado Court of Appeals and Colorado Supreme Court, and the United States Court of Appeals for the 10th Circuit. (And that is just for civil cases, there are criminal divisions in most of those courts that follow different practices, Denver Juvenile Court, the Roman Catholic Church's Canon Law Court for the Diocese, and several varieties of administrative courts for unemployment, social security, immigration and other matters also in the same compact physical area that I don't mention.)
All of those courts are in physically located within walking distance from each other in the same county and same zip code.