This takes lots of patience. Hopefully you still have the little hollow stamped steel cups that the rear bows fit into before you place them in the side rails. As I recall, I started positioning the bows from the front and worked my way to the rear. The front bow has a choice of two set points. It will be obvious which one to use. The front and rear get stapled into place before the sides. Keep pulling the material tight as you staple. Using a hair drier helps a little to make the material a little more pliable while you do this, but do this only as a last resort. Staple the sides last. Then you can squirt the headliner with a water mist via a spray bottle. Put the car outside with the windows up on a hot day. This should allow the headliner to "set" a little better and cause some wrinkles to disappear. Then readjust the liner, trim the edges and install the moldings.
For a stapler, you might want to try the small "Arrow" brand compression stapler that most hardware and Walmart type stores sell. I think I used 1/4 or 3/16 staples. Double sided tape will not work. There is far too much tension needed to keep the liner in place. Prior to doing anything, make sure that the tack strips are good enough to reuse. If not, go to an auto upholstery shop and get some replacements.
BTW, the Osborn books even show how many staples the production line workers were to install in the tack strips!