How does Tokyo Drift fit into the time line?

Simply put, the story of Fast and Furious is not in the order that the movies are released. A bit of this post is a little speculative since one of the movies is in pre-production, but the cast has already been confirmed. Obviously there are some spoilers below tying it all together.

The first movie - The Fast and The Furious (2001), ends with Brian O'Conner letting Dominic Torreto make a run for it. For this, Brian also damages his career but he has got a taste for street racing and pursues this, moving from Los Angeles (the location of the first movie) to Miami (the location of the second movie) and continuing with street racing.

The second movie - 2 Fast 2 Furious (2003), ends with Brian O'Conner and Roman Pearce successfully completing their undercover work, resulting in the antagonist Carter Verone being arrested and their names being cleared.

This then leads onto Fast and Furious (2009), in which Brian O'Conner is now back with law enforcement and is now a detective, working with Torreto to bring down a Mexican drug cartel leader, Braga. By the end of this movie, there is a clear established trust between Torreto and O'Conner, which culminates when Torreto is sentenced to prison and O'Conner and Mia Torreto breaking him out and going on the run. This leads directly into the fifth movie.

Fast Five (2011) starts off with the closing scene of Fast and Furious, and results in the crew attracting the attention of Agent Hobbs, "the guy that the FBI call in when they need to get their man". Due to events in the movie, Hobbs and Torreto's crew briefly align to take down a Brazilian drug lord and the movie ends with Hobbs giving Torreto 24 hours before he comes after them.

Fast and Furious 6 (2013) takes place sometime after Fast Five with Hobbs asking for Torreto's help in bringing a rival gang to justice, using Letty's presence in the gang to peak his interest and ends with Han returning to Tokyo after Gisele is killed saving his life as this is where they were going to settle down after stopping Shaw's crew.

Furious 7 ties the entire franchise together, starting part way through 2006's The Fast and the Furious: Tokyo Drift and featuring scenes that take place during the ending cameo from Tokyo Drift. The seventh Fast and Furious and Tokyo Drift occur after Fast and Furious 6.

Here is a full Fast and Furious Timeline as

1. The Fast and the Furious (2001)
2. Turbo Charged Prelude (2003 Video)
3. 2 Fast 2 Furious (2003)
4. Los Bandoleros (2009 Short Film)
5. Fast & Furious (2009)
6. Fast Five (2011)
7. Fast & Furious 6 (2013)
8. The Fast and the Furious: Tokyo Drift (2006)
9. Furious Seven (2015)
10. The Fate of the Furious

Source: Wikipedia

For knowing how and why this happened refer related question:

Why does the Fast & Furious franchise have a chronological order different from the release order?

At the end of Fast 6 they show the same clip from Han dieing in Tokyo Drift, but you see Jason Statham get out of the car that hit Han's. So seven will take place with Dom going to Tokyo (assuming) since he shows up in the end of Tokyo drift

Tokyo Drift felt really out of place in the timeline. Nothing seemed to add up because it was assumed the events occurred either completely independent of Dom's realm, or perhaps directly after 2 Fast 2 Furious based on Dom's appearance at the end of the film.

The writers did an amazing job re-introducing Han into the big picture by giving him a small yet effective role in Fast and Furious; despite his short time on screen, Han is established to be a valuable friend and associate of Dom's as he is an incredibly skilled driver at the very least. Han reprised his role in Fast Five and in Fast 6 on a much larger scale, establishing a relationship with Gisele. The events in Fast 6 now opened the door for Tokyo Drift to entire its place in the timeline; Han leaves the crew to pursue his own personal affairs after the death of Gisele.

In Tokyo Drift, Han establishes himself and takes on the "Dom" persona of the street-racing and crime scene; he's well respected by friends and enemies and only drives competitively when he truly needs to. Backtracking to the important exchange between Brian and Mia in Fast and Furious - Dom is respected because he lives by his own code. His strong and influential presence effects those around him - Brian and Han included. This is made evident by the conversation Han and Sean have at the top of the building, when he explains what he finds important (trust) and why he drifts. Han, like Dom, has established his own code.

In later events in Tokyo Drift, Han races DK in the streets and dies in an apparent racing accident. However, it is revealed at the end of Fast 6 that it was no accident; Shaw's brother Ian was behind the wheel of the car that struck Han, killing him as revenge for the death of his brother, which Han was partially responsible for. He phones Dom and lures him out to Tokyo, which likely explains Dom's cameo appearance at the very end of Tokyo Drift.

So, Tokyo Drift now has a clear time-stamp in the entire franchise. The events of Tokyo Drift happen after Fast 6 (perhaps not immediately after, as Han would have needed some time to establish himself in that city), which tells us that at least some of Fast 7 will be set in Tokyo. Some other questions that come to mind is if anyone in the Tokyo Drift realm will be included in Fast 7; the notable figures are obviously Sean, Twinkie, and Neela, but none of them really have the chops to hang with Dom and his crew.

Perhaps the most exciting prospect of Fast 7 (to me) is that the dynamic has been completely changed; Dom and Brian have been depended on to apprehend a villain or steal a lump of money, but this time, they are being hunted by Ian Shaw (Jason Statham), which shows his ruthless personality by stalking and killing Han.

Watch the movies in this order if you want to know:

• The Fast And The Furious [2001]
• 2 Fast 2 Furious [2003]
• Fast And Furious [2009]
• Fast Five [2011]
• Fast and furious 6 [2013] (don't forget to watch the mini clip at the end!)
• The Fast And The Furious: Tokyo Drift [2006]