I suppose I will impart my newfound knowledge, then.
Cloth in the BGE is slightly more complicated than cloth in the render engine.
1. Make your cloth object, and remember the cloth only bends on vertices (so a single plane won't do much)
2. Set the Physics to "Soft Body", deselect "Shape Match", and set the "Collision Bounds" to "Triangle Mesh"
You now have a bit of cloth. To make it pinned to something, you need a rigid body joint
3. Add an object or empty. The cloth vertex closest to this object will get pinned in place.
4. Add a "Rigid Body Joint" constraint to the object, and set the "Target" to whatever your cloth is named. Voila!
You can add multiple joints if you want. You can also offset the rotation center of the joint using the X, Y and Z fields (click "Display Pivot" to see where the cloth will hang from)
