A garment steamer is a water tank, a hose, and a heated head on a pole. Drain it fully so it cannot leak, then bundle the parts, and it packs down small and travels dry.
Pro tip: Run the steamer empty for a few seconds after draining to clear the last water from the line before packing.
Watch out: Never pack a steamer with water still in the tank; it leaks onto everything and breeds mold and mildew.