After you have set up the deflection mesh for the frame range you intend to run the simulation (including animating that mesh via armatures), you can now tell the cloth simulation to compute (and avoid) collisions. Select the cloth object and in the Object tab, Physics tab, set the Start and End settings for the simulation frames you wish to compute, and click the Bake button.
Cache settings for cloth are the same as with other dynamic systems. See Particle Cache for details.
If you move or edit the cloth object after you have already run the simulations, you must clear the cache; otherwise, Blender will use the position of the current/cached mesh's vertices when trying to represent where they are.
Subdivision Surface Modifier
A bake/cache is done for every subdivision level so please use the equal subdivision level for render and preview.
You cannot change Start or End without clearing the bake simulation. When the simulation has finished, you will notice you have the option to free the bake, edit the bake and re-bake
Editing the Cached Simulation
The cache contains the shape of the mesh at each frame. You can edit the cached simulation, after you have baked the simulation and pressed the Bake Editing button. Just go to the frame you want to fix and Tab into Edit Mode. There you can move your vertices using all of Blender's mesh shaping tools. When you exit, the shape of the mesh will be recorded for that frame of the animation. If you want Blender to resume the simulation using the new shape going forward, select Rebake from next Frame and play the animation. Blender will then pick up with that shape and resume the simulation.
Edit the mesh to correct minor tears and places where the colliding object has punctured the cloth.
If you add, delete, or extrude vertices in the mesh, Blender will take the new mesh as the starting shape of the mesh back to the first frame of the animation, replacing the original shape you started with, up to the frame you were on when you edited the mesh. Therefore, if you change the content of a mesh, when you press Tab out of Edit Mode, you should unprotect and clear the cache so that Blender will make a consistent simulation.