FWIW....I do screen repair at my job (about 500 per year). That ACE video is fine but there are few things that can help prevent problems. That metal tool is perhaps the worst. Try to get the plastic one and try to get one with the large wheels. The metal one tends to cut the screen. There are two wheels. The thin "blade" type is used to make the groove in the screen before inserting the spline. You want to hold the window side of the screen as you insert the spline so it does not pull the fabric from the window side but from the overlap side. Do not pull the screen tight. A little bit of looseness is preferable. Before screening lay the frame vertically along a flat surface to check if it's not warped. If it is, carefully try to straighten it out by dragging it along an edge multiple times to remove the warp. But do it slowly and with out too much pressure. You don't want to kink the frame. Keep in mind that just through time and sun exposure the screen will harden and shrink and pull the frame into a warped position. It will have memory and if pulling the screen tight it will warp again with the new screen even with straightening it.
Screen repair is whole new ball game from rescreening and will most often require new corners. Some corners are just a slip in while other must be drilled out. There are hundreds of screen corner and you must get the right one. A screen with a mitered corner is stronger and usually will have a metal corner that won't be exposed to the sun's UV.
