It was once the case that if you wanted to do serious video editing, your choices were limited. Outside of expensive commercial options from the likes of Sony and Adobe, you'd have to make do with Windows Movie Maker... or worse. These days, free options abound. The hardest part is actually picking one.
Like any creative tool, you have to find one you like and the only way to do that is to sample a bunch. Everyone has their own requirements, be it support for full resolution exports, to a simple editing interface.
I came across a thread on /r/gamedev on Reddit where the poster asked for suggestions on editing clips from their game, where easy-of-use, learning curve and most importantly, no cost, were essential.
I've taken the liberty of collecting those suggestions and listing them below. Of note, almost all the options support all three major platforms. I also had no idea Blender comes with video editing capabilities.
Blackmagic Davinci Resolve
From the website: "Originally designed for Hollywood’s elite colourists, DaVinci Resolve has been used on more feature films and TV shows than anything else because it lets you create images that are simply impossible with other tools. ... DaVinci Resolve 12.5 is the world’s most advanced editing and colour grading system for independent users working on SD, HD and Ultra HD projects." — Windows, Linux and OS X.
OpenShot Video Editor
From the website: "OpenShot Video Editor is a free, open-source video editor for Linux. OpenShot can take your videos, photos, and music files and help you create the film you have always dreamed of. Easily add sub-titles, transitions, and effects, and then export your film to DVD, YouTube, Vimeo, Xbox 360, and many other common formats." — Windows, Linux and OS X.
From the website: "Shotcut is a free, open source, cross-platform video editor for Windows, Mac and Linux. Major features include support for a wide range of formats; no import required meaning native timeline editing; Blackmagic Design support for input and preview monitoring; and resolution support to 4k." — Windows, Linux and OS X.
From the website: "Kdenlive is an acronym for KDE Non-Linear Video Editor. It is a free software (GPL licensed) primarily aimed at the Linux platform. It also works on BSD and MacOS as it relies only on portable components (Qt and MLT framework). Non-linear video editing is much more powerful than beginners' (linear) editors, hence it requires a bit more organisation before starting. However, it is not reserved to specialists and can be used for small personal projects." — Windows, Linux and OS X.
From the website: "VFX professionals say: 'Probably the best tracker in the market'. Blender includes production ready camera and object tracking. Allowing you to import raw footage, track the footage, mask areas and see the camera movements live in your 3D scene. Eliminating the need to switch between programs." — Windows, Linux and OS X.
HitFilm 4 Express
From the website: "Tailor HitFilm 4 Express to your specific filmmaking needs with special features and effects. Pick and mix from over ten different add-on packs. Put your idea in motion." — Windows and OS X.
One of the above will almost certainly meet your specific needs, though there's only one way to find out. Time to start experimenting.