Export the movie as a File to your desktop and, when the export box pops up choose the highest resolution option that you have available, with Better Quality Compression and High Quality. For example
There is a Best (pro res) setting, but I wouldn't use that. It gives you a 4x larger file size and is mainly intended for professional style editing. The human eye likely wouldn't even notice a quality difference unless one zoomed in on the pixels. So I would stick with "High" for the Quality setting rather than Best (pro res).
The Mp4/AAC movie that you will get with all settings other than Best Quality (pro res) will be high quality and pretty much universally compatible with all platforms and devices.
You didn't mention what resolution your movie was recorded in. If you try to export out at more than one level higher resolution usually the results are poor. So, you can go from 720 to 1080, or 1080 to 4k, if you have those export options, but don't go from 720 to 4k, as that would be two levels higher.
-- Rich