I was also going to suggest OBS, however I am also struggling to find a good free video editing software
Viewing post in Mini Challenge: Make a trailer for your game.
There's always Windows Movie Maker (/equivalents) if you're on Windows. It's really not bad for basic editing. I remember hearing that Macs also come with a basic video editor?
There's Lightworks if you want more special effects (free version is limited to mp4 exports & needs to be renewed weekly). I'd recommend Filmora, but the trial version's watermark is just too much to ever recommend for trailer work. Blender (a free 3D modeling software) has some awkward video editing and export tools as well.
There might be better ones out there I'm not aware of. At the very least, there's dozens of miscellaneous freeware junk floating around from old college programming assignments.
If you honestly want to work with a lot of text and get some nice effects, etc. without dishing out money for a video editor, though, you might be best off just working in your game engine of choice. ex: Make a new branch, hard code the trailer effects there with the right timing, then record what happens. (That workflow isn't always an option, I know, but it is fun.)
Isn't it? I never thought about it until I was looking into cross-system video support in GameMaker:Studio. (I wanted to run a trailer the first time the game launches; it's a nice touch for those who picked it up from bundles / etc. and waited a while to see what it was.)
But it's apparently really hard to get all the right codecs playing nice on multiple systems, so there's not much support for videos in that engine. A lot of users on the forums over there recommended building cutscenes and trailers in-game as a result.
Turns out that's actually a really useful approach sometimes haha. You much have way more control over the scene in an engine than you do in most editing programs.