ironically, one of the signs I was having problems (though I didn't realize it at the time) came when I went to see an old 50's 3D movie. I had to watch the movie for a long time -- say half an hour? -- before the 3D effect worked for me. That was a sign my binocular vision was failing, but I didn't realize it.
The main therapy consisted of viewing red/green or polarized anaglyphs (trademarked as Tranaglyphs ™), while the therapist adjusted the separation between them. Since my left eye was turning outward, at first I could only fuse the two images when they were widely separated. With repeated exercises, over several weeks, I was finally able to fuse the images at normal separation. After each session, I could tell that my vision was taking on a little added depth -- and an hour or two later I would get a real hammer-between-the-eyes headache. After the whole therapy sequence was finished, it still took some time to re-adapt to full binocular vision, and my eyes tended to tire easily.
A big prerequisite to successful therapy, in my case, was having my lens prescription reduced by a doctor who was very careful not to over-prescribe the lens strength. Many ophthalmologists tend to over prescribe, and if you are young and nearsighted, your eyes will adapt to the overcorrection. Over a period of many years, I had accumulated quite a lot of overcorrection in one eye, causing that eye to suffer so much fatigue that it would stop focusing properly and my brain would simply suppress the image from that eye. It was a real shock to discover one day that I could cover my left eye and leave my vision almost unaffected -- the image from that eye was not being processed much at all. Some doctors routinely check for overcorrection, others -- not so much.
Sue Barry's book describes some of the other treatments used. She had been stereoblind her whole life, unlike me, so her doctor started her off with more basic therapy than I needed. I thought the bead-on-two-strings would have been a good home exercise for me, but I didn't learn about it until after I no longer needed therapy.