There are 3 time periods within the film's story and they are distinguished primarily by the protagonist's appearance. We have the young man:
1) Unshaven with long hair,
2) Clean shaven with short hair,
3) Clean shaven with short hair and a bruised face.
The story jumps from one timeline to another, all moving forward through each segment.
There are also the framing sequences (opening and closing the film) which take place after the internal story. The internal story plays as if the young man is describing it to the older man. It does, however, include a few sequences that neither the young man nor the older man are aware of, and these serve to reveal things to the viewer that the young man does not know. These "reveal segments" give the movie its "twist" at the end.
The movie starts during the credits with a "teaser" (the teaser seems to be a "trademark" of a Nolan film; it is a generally a clue/hint of a larger truth and indication that there is more to the film than we will see directly). The teaser is hands putting on latex gloves, opening an empty box, and add some items to it. We will see similar gloves and the boxes and items later during the film.
****Warning: some spoilers ahead****Don't look unless you want to be spoiled.
After the credits we start with the opening framing sequence in a voice-over. We see a montage of the young man in "Timeline 1" unshaven with long hair as he introduces his story and details it to the older man. Timeline 1 starts with the young man following a man named Cobb.
As the framing sequence continues, we see the young man in the "present" (clean shaven, short hair and bruised) talking to the older man.
The voiceover continues in Timeline 2 with the young man (clean shaven, short hair) looking at items from the box we saw earlier, and then following a blonde as she goes from an apartment to a nightclub.
This is followed by Timeline 3 (clean shaven, short hair and bruised) as we see the young man seemingly after a fight, coughing latex gloves out of his mouth.
The framing sequence introduces the premise, and indicates the three timelines we will be seeing throughout the movie. It shows that the framing sequence occurs shortly after Timeline 3 and links back with items from the teaser.
Segment 1. The internal story starts by continuing Timeline 1, started in the framing sequence. After a bit of time, we cut to continuing Timeline 2 from the framing sequence, then finally Timeline 3 continues.
Segment 2. Continue Timeline1, continue Timeline 2, continue Timeline 3.
Segment 3. Continue Timeline 1, continue Timeline 2 (this contains a flashback as the blonde describes a murder in her flat), continue Timeline 3.
Segment 4. Continue Timeline1 (during this segment Timeline1 ends and transitions to Timeline 2 as we see the young man shave and cut his hair), continue Timeline 2 (contains "Reveal 1" where we learn Cobb and the blonde are working together to set up the young man); continue Timeline 3.
Segment 5. Continue Timeline 2 (during this segment Timeline 2 ends and transitions to Timeline 3 as we see the young man get beat up by Cobb and have gloves put into his mouth; also contains "Reveal 2" where Cobb tells the blonde more details about the setup); continue Timeline 3-blonde tells young man about setup.
Closing framing sequence. The young man explains what he knows and how he was set up by Cobb to the older man. (Contains "twist" in "Reveal 3" where it is revealed that Cobb is actually setting up the blonde. The young man is set up not for the reasons Cobb gave the blonde, but to implicate him in the murder of the blonde, whom the bald man wants to have killed, as she was blackmailing him).
