Cloth Simulator

The basic principle behind using the cloth simulator is to add a Cloth physics element (and modifier) to the cloth object, and add Collision physics element (and modifier) to the interacting objects.  In this demonstration, I'll show how a tent cover (sheet) can be draped over a metal frame. The frame is shown below.

For the frame (and also the ground) go to the Physics tab, and click on Collision.  No particular settings need to be adjusted here.

Now create a Grid object (which will be the sheet) and add a SubSurf modifier (to give more folding definition).  Now, the cloth objects Physics tab, click on Cloth.  For this one you do want to change some settings.  You can choose a preset material rather than trying to set all the different parameters.  And also, to make the collision realistic, you'll want to enable Self Collision.

Once the cloth (green) is in place, hovering above the frame, simply press [Alt+a] to run the animation, and the cloth will slowly float down onto the frame and wrap along it, influenced by gravity.

If you want the mesh at a specific folded frame, simply jump to that frame and apply all modifiers from top to bottom.  Applying the Cloth modifier will cause the mesh to be permanently deformed according to the simulation and can be used accordingly.

As well the animation of the falling cloth can be captured if that is desired.