Editing video is a hot topic for free software, in fact GNU/Linux still lacks stable tools to perform the most popular non-linear editing technique, but development is rapidly evolving.
Inside dyne:bolic you'll find the two best applications that are available for the task: Cinelerra implements a canonical approach to non-linear editing, while LiVES is a new promising application using an almost-linear "cut and paste" approach and supports more video formats for input files. Both applications are being actively developed during the time being and will require a bit more patience and attention to be properly used, given the complexity of the task they accomplish.
You can be introduced to Cinelerra by the manual available on http://manual.cinelerra.org.
LiVES uses large amounts of scratch space during processing. By default it will try to use the /tmp directory, which is located in memory when d:b first boots. There are several ways to improve this. Using a 'nest' file replaces the memory version of /tmp with space from the nest, so if you make it large enough, that can solve the problem. You also can set a different location for the temporary files in the LiVES preferences. If you set this to point to a real disk, things go much smoother.
Also consider that d:b will boot with 64 Meg of memory, but it will be limited in what you can accomplish. Video editing is a memory intensive activity. Linux systems generally use virtual memory in the form of 'swap' space to extend capabilities beyond the physical memory. d:b will use a swap partition if it exists, but if you are hosting on a system without a writable partition, there won't be a Linux swap partition to use. It is possible to create a swap file on a FAT formatted hard drive.
For converting between video formats its included the powerful Transcode tool, which is a commandline application that can be scripted to convert large number of files or easily accessed via a graphical interface.