I want to convert some
.avi videos to a lower resolution, both to considerably shrink the files' sizes and to make them easily viewable on a smartphone. How can I do the conversion? I have ffmpeg installed on a desktop running Ubuntu.
I recommend you download Handbrake, which is basically a nice (subjective!) interface which will allow you to convert between formats easily (including ffmpeg).
It includes presets for mobile devices and if you are uncomfortable using ffmpeg directly, you should like this program.