Quickest way to claim a business on google?

Search the business name on Google Maps, open the listing, and look for the "claim this business" / "own this business?" link. If there's no listing, add one through Google Business Profile. Then verification, which is the slow part. It might be phone, email, a video of the premises or a postcard depending on what Google offers you, and you don't get to choose. Make sure the address matches exactly what's on your signage and site or the video one tends to get rejected.