It's fair to say that Freud was never that interested in the grunt work of being a doctor; he didn't take his medical exams until the spring of 1881, a couple of years after many of his contemporaries; this was largely because he had been spending time in the scientific laboratory of the physiologist Ernst von Brücke doing research on nerve cells; Freud only became a doctor when he found himself a fiancee, Martha Bernays, and von Brücke informed him that there wasn't a permanent place in his laboratory for him until others retired, which would be some time off.

After qualifying as a doctor, he worked at the General Hospital in Vienna, in the role of Aspirant, which in practice meant that he was a kind of clinical assistant, who 'sampled' various departments, from surgery to dermatology to psychiatry; he rose up the ranks in the clinic in his three years there, but remained in assistant roles. There's no real reason for any of his patients to remember him from this point; as an assistant he was relatively anonymous, doing drudge work while dreaming of scientific fame (Freud's letters to his fiancee at the time make it very clear he really was obsessed with making it as a famous scientist).

He was most prominent during this period for a now-infamous paper proclaiming the greatness of cocaine, which he had used to treat a friend who had a morphine addiction; Freud thought that the cocaine seemed to remove the addiction to morphine, and it was only after the paper was published that Freud began to notice some of cocaine's side effects in his friend, like psychosis and addiction. After this, he promptly moved to France to study with Jean-Michael Charcot, famous for putting hypnotisability at the centre of psychopathology (e.g., people who were hypnotisable were almost certainly hysterical, or had other disorders). Freud returned to Vienna to start a private practice initially based on being Charcot's guy in Vienna; however, Charcot's stocks plummeted in the late 1880s as other doctors showed that the general population was generally quite hypnotisable, and Freud stopped defending Charcot in 1889. But by this point Freud was definitely a psychiatrist, treating neural disorders. Which of course is still being a doctor. The boundaries between neurology and psychiatry at this point were quite porous; Freud's first book was a technical book on aphasia (neuropsychological disorder resulting in problems with linguistic communication).

There is actually little evidence that Freud's techniques worked in the case studies that he published; for all his theorising, Freud only published 6 detailed case studies, and only in 2 of them ('Wolf Man' and 'Rat Man') did he claim to have cured the patients, and Sulloway (1991) finds that those two cases are much more problematic than Freud claimed them to be. A letter by Freud to Carl Jung in 1908 claims that "I have no case that is complete and can be viewed as a whole" (i.e., a successfully cured patient)

Generally Freud's psychiatric patients, as he developed his theories, weren't as impressed by his treatment techniques as he was. One case study he discussed was 'Elisabeth von R.'; when historians tracked down who she was, her daughter said that her mother had told her that Freud was "just a young, bearded nerve specialist they sent me to" who had tried "to persuade me that I was in love with my brother-in-law, but that wasn't really so." Nonetheless, von R. symptoms did cease after talking to Freud, though she discounted his role in that.

With the Rat Man, Freud discussed the case at a conference in 1908; the Rat Man basically had what now looks like obsessive-compulsive disorder, and was in reality a man named Ernst Lanzer. Sympathetic observers of the case have pointed out that Freud claimed at the conference to have treated Lanzer for eleven months, but in fact he only treated him consistently for three months and then sporadic checkups for a few months after that; Freud also misrepresented the patient in various ways to make his analysis sound stronger. Freud's therapy does seem to have lessened Lanzer's symptoms, but Lanzer broke off analysis early, and Freud seems to have privately viewed it as a failed case despite his public pronouncements.

With the Wolf Man, which Freud discussed in 1914, his real name was Sergei Pankejeff, and Pankejeff lived a long life until 1978, and was located by a journalist, Karin Obholzer, in Vienna in the early 1970s for a book that was published in 1982 (Wolfman: Conversations with Freud's Controversial Patient). According to Sulloway's 1991 article,

From Obholzer's conversations, we learn that the Wolf Man himself considered Freud's interpretation of his famous dream to be "terribly farfetched" and that he also felt betrayed by Freud, who had promised him that he would one day actually remember the traumatic event that had made him ill.

We also learn from Obholzer's interviews that the Wolf Man was by no means cured, either by Freud or by subsequent analysts. He remained a compulsively brooding personality with endless self-doubts; and he himself strongly disputed the analytic myth of his "cure." "That was the theory," he told Obholzer, "that Freud had cured me 100 percent...to show the world how Freud cured a seriously ill person. . . . It's all false." As the eighty-six year-old Wolf Man plaintively concluded of his psychoanalysis: "In reality, the whole thing looks like a catastrophe. I am in the same state as when I first came to Freud, and Freud is no more."

It should also be pointed out that, basically, Pankejeff's interviews with Obholzer were only published after his death; he had 'free' psychoanalysis for many years after Freud's initial treatment, and later in life, he'd effectively been paid off by the powerful psychoanalysis institute in Vienna to keep quiet about the failure of the analysis.

"Instead of doing me some good," he exclaimed to Obholzer, "psychoanalysts did me harm," adding plaintively, "I am telling you this confidentially."

Sources:

Frank Sulloway, 1991, 'Reassessing Freud’s Case Histories: The Social Construction of Psychoanalysis' in Isis

Frank Sulloway, 1979, Freud: Biologist Of The Mind

Peter Gay, 1988, Freud: A Life In Our Time

Thomas Leahey, 2004, A History Of Psychology: Main Currents In Psychological Thought (6th edition)