You'll likely need to remove or partially remove the glove box to access it. It's usually a small-diameter hose or tube that runs down towards the floorboard. Be prepared to get slightly damp or wet, as it will contain condensate.
Since there can be variations, searching for a 1999 Chevy Suburban repair manual or looking at online forums dedicated to this vehicle model (e.g., on sites like ChevyTalk or similar forums) might provide you with pictures or more precise instructions.