Action cameras are overwhelmingly supported by the H.264 codec which is currently the most widely used (i.e. with Blu-ray players, and for uploading on YouTube etc.). Editing can be done with virtually any program, including with programs that are often integral to the operating system - Windows Movie Maker (Windows) or Imovie (Mac).
When selecting an editing program, considerations such as user preferences and experience should be made. Some programs are free, while others are paid, some are simple to use while others are far more complex.
Here are some interesting links and videos:
http://technet.idnes.cz/strih-videa-cxm-/software.aspx?c=A160120_194035_software_dvr
http://stah.cz/magazin/5-nejlepsich-programu-pro-upravu-a-strih-videa-zdarma
http://technet.idnes.cz/v-cem-strihat-video-0o0-/software.aspx?c=A140806_184728_software_dvr
Most programs that are not free can be downloaded as trial versions for free, time-limited testing without any limitations.
Among the most popular and easy to use program is PINNACLE, the sophisticated and professional SONY VEGAS programs and the more demanding Adobe Premiere (PC) / FinalCut (Mac).