How can I attach a large satin applique to a skirt?
The "iron-on stuff to stick them together" that you'd heard about is called fusible interfacing. For satin, you will be looking for a "lightweight" or "feather" interfacing that has heat-activated adhesive.

It only needs a second or less of contact with an iron to melt to fabric, and  will not bleed through like glue. I recently used it to attach lace to satin, and it performed beatifully. Satin to a thicker base fabric should be similarly successful. Just make sure your iron isn't on the hottest setting -- neither the fabric nor the interfacing need that much heat :)