There is a limited amount of video editing software available for the Linux operating system, particularly if you are striving to keep it free and open source. However, a mixture of different programs with outstanding features could be exactly what you're looking for.
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With the launch of the GNU project in 1983, the Free Software Foundation (FSF) undertook the massive endeavor to create and provide a massive store of open source software that would entirely eliminate the need for software that isn't free (free as in freedom, not necessarily free of cost). Over 25 years later, the Linux and open source communities have very nearly realized that goal, with thousands of freedom enthusiasts using nothing but open source software and operating systems.
However, there is one software genre that has been noticeably lacking (at least in options and volume): Video editing software. There are a few programs out there, but their features and capabilities tend to leave something to be desired when compared to the commercial options available on the Windows and Mac operating systems. There are those die hard enthusiasts, though, that have managed to come up with a process by which they can meet their video editing needs utilizing only open source software, that is incidentally free (as in cost) as well.
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Free Open Source Software for Linux Video Editing
The generally agreed upon best method for video editing with open source software on the Linux operating system involves two unique programs.
The Kino video editor project, like most open source programs, is currently and always under development. The stated goal of the project is to be a viable choice for all video editing purposes, which includes being simple, reliable, and able to import/export in a variety of useful formats. While Kino could very well be what you are looking for in a free video editor for Linux, the general consensus is that Kino should be used in conjunction with another program called Cinelerra in order to achieve the best results.
Kino has full support for Firewire (IEEE 1394) DV capture and for recording back to the camera. This makes it the preferred method for "grabbing" video off of the camera and saving it to your computer to be edited. From there, though, most enthusiasts and professionals then abandon Kino in favor of Cinelerra for the actual editing process.
Cinelerra is considered the most advanced open source program for video editing, fully featured for layered framerate - and resolution - independant video editing, as well as creative effects. It has been likened to a combination of Adobe Premiere Pro and Adobe After Effects, only open source and built for the Linux operating system. Cinelerra is sold as part of a software bundle from Linux Media Arts but is also available in a compilable "Community Version" (Cinelerra-CV) which is free of cost.
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Commercial Video Editing Software for Linux
There was once a full featured commercial video editing program that supported both the Linux and Windows operating systems, called MainActor, produced by MainConcept. In 2007, the decision was passed down to discontinue the production of MainActor. Later that year, DivX took over MainConcept. While MainActor is no longer "officially available or supported" there is a lively unofficial forum dedicated to continuing the usage of what most saw as the best Linux video editing software available, despite coming with a price tag of nearly 200 USD. If you can manage to get your hands on a copy of MainActor, the Unofficial MainActor Support Forums will no doubt prove to be a crucial resource.