This is easier to understand if you have seen the anime Dragon Ball Z (and if you haven't, then you obviously had a very different childhood than me). Team Four Star does not add any new images to the footage they are working with. They simply edit each scene so that the order of events are rearranged, or cut out entirely. This, combined with the new dialogue that they write themselves, makes it possible to create a new series that has an entirely different plot, tone, characters, and themes.
When they first started out, back in 2008, you can tell that the process of rearranging clips of Dragon Ball Z into a new, yet still coherent story, was a work in progress. The early episodes, while still funny, are not as seemless or professional looking as more recent ones. Team Four Star has been producing Dragon Ball Z Abridged for over 5 years now, and you can tell just how much they have improved. If you are familiar with Dragon Ball Z already, I would recommend starting with Episode 31 (linked above). This episode represents the start of the 3rd "season" and I think would be more likely to hook new fans. People already familiar with Dragon Ball Z (which I imagine represents 99% of Team Four Stars audience) will recognize the characters and the major events of the plot, but they will also see how much more adult and clever the dialogue has become.
I think the fact that Team Four Star has updated a beloved anime for an adult audience is the key to their success. There are many millennials who grew up with DBZ and have fond memories of it. Team Four Star has taken that anime and inserted adult themes and language very successfully. It hits all of the nostalgia notes of the original anime, yet provides the perverse pleasure of hearing Bulma shout "you motherfucker!" at Vegeta. The ability of three people (who all live in separate states) to reedit and redub a cartoon with professional quality equipment was not feasible until recently. The democratization of art through technology is opening all kinds of new opportunities for artists to get their name out.
The Official Team Four Star Website can be found at:
The Website is badly in need of a redesign. On a recent video Team Four Star promised a new, more polished layout soon, so hopefully by the time you click the link, the new redesigned website will be up.
The Team Four Star YouTube Channel can be found at:
This is where most fans go. The YouTube channel actually has more content than the website, and is easier to access.
Team Four Star also puts out an abridged series based on the anime Hellsing Ultimate, though at a much slower pace than they put out DBZ Abridged episodes. This series is extremely funny in its own right, though it does not get nearly the same attention since Hellsing does not have a the cultural cache of DBZ.