when he finds out that he actually is tyler, they go back in time and show clips, one of them being him fighting with himself. if you go back and look at the clips closely you'll notice it ^^
but the shooting himself.. it's however you interpret it. it may help reading this:
"Due to the graphic nature of the gunshot at the end of the film, many viewers believe that The Narrator actually kills himself and therefore only 'imagines' the last few moments of the film as he dies. Director David Fincher does acknowledge on his DVD commentary that the gunshot causes confusion because it is so over the top, appearing to actually go through The Narrator's jaw. However, The Narrator is depicted as supposedly having suffered no serious injury, and importantly, if you look at the scene closely, you can see the bullet ricochet off his jaw and bounce back out of his mouth, thus explaining why the apparently fatal injury was not in fact fatal.
It is perhaps worth pointing out that in the novel, The Narrator's face is much more grotesque than in the movie. In the novel, The Narrator already has a hole in his face due to the fight with Tyler. The gunshot then hits the other side of his face, causing another hole, which connects with the original hole, creating a huge, joker-like grin. But like in the film however, the wound, despite its superficial seriousness, is not fatal.
To examine the scene further, there are all sorts of theories as to the symbolism of the gunshot and its effect, primarily in relation to the death of Tyler. Some argue that the gunshot was The Narrator's final way of 'hitting bottom' as Tyler wanted, so therefore Tyler ceased to exist, as he was no longer needed. By attempting suicide, The Narrator is obviously no longer afraid of death or pain (which is what Tyler is trying to teach him during the scene where he pours lye on his hand). For this reason, Tyler's role becomes obsolete, because The Narrator had only created Tyler initially so as to express the more reckless nature which he had tried to repress. Others argue that the gunshot represents The Narrator's absolute rejection of Tyler, thus killing him. This is based on the concept that the bullet did in fact pass through the Narrator's head, but since he was two people, it was Tyler who was killed and not The Narrator (hence the exist wound in the back of Tyler's head). In this sense, it is significant to note that the affliction from which The Narrator seems to be suffering, Dissociative Identity Disorder (DID), has been known to be 'cured', or otherwise eradicated, if the patient experiences a traumatic event; receiving a gunshot to the face undoubtedly counts as a traumatic event. Yet another argument is that rather than Tyler dying and The Narrator surviving, the two characters merge. After the gunshot, The Narrator has clearly become a different person, evidenced primarily by the fact that he stops denying his feelings for Marla. Additionally, the flash of the penis just before the credits would seem to support the idea that Tyler is still alive 'somewhere', hence the merging theory. "
http://www.imdb.com/title/tt0137523/board/thread/128777407?d=128779204&p=1#128779204