The opening scene of the movie happens in Limbo where Cobb (Leonardo DiCaprio) goes to fetch Saito. This actually happens moments from the ending of the movie.
Inception is inserting an idea into someone's head. This process cannot be obtained through the normal dream within a dream phase. It takes a multi-level dream sequence to happen.
Inception cannot be done with a complex idea. It can only be done with the simplest forms of ideas and the subconscious mind of the subject grows the idea inside.
In any phase of the dream, the dreamer can access the subconscious of the subject. The dreamer is the one who designs the dream and the subject is the person who populates the dream.
The reason why Cobb can't be the dreamer is because he cannot control his subconscious properly. His deceased wife always haunts him in the dreams.
Ariadne (Ellen Page) designs the sequence of dreams that helps the group implement the idea in Fischer's head. However, Cobb cannot know about the architecture of the dreams because his subconscious might work against him.
Eames (Tom Hardy) is an identity thief who can become anyone in the subconscious of the mind. He helps Fischer obtain the idea that his father wanted him to do something.
Cobb used inception before but by accident which led his wife to think that the living world is the actual dream and vice-versa.
Saito dies in the 3rd phase of inception which leads him directly to Limbo, which is the final stage of the dream. In Limbo, five minutes of dreaming are equal to around 50 years. This is why everyone is scared of it.
Cobb is eventually stabbed and dies in the dream. His purpose now is to return Saito back to reality. When he arrives there, he finds that Saito has grown very old. However, this is something that Cobb has also gone through with his late wife.
When Saito wakes up, he makes the phone call as promised to permit Cobb's access to the United States. The inception has been done and Fischer has a plan that was implanted in his head.
Cobb's totem continues spinning at the last scene of the movie. However, he is back to reality and that is a scene from a previous time.