Once you have installed FFMPEG, restart Audacity. It will automatically try to detect FFMPEG.
Caution: Audacity currently supports FFMPEG's libavformat in version 55, 57 and 58. If your distribution ships with a different version, it may not get detected, or may not work correctly. In that case, you may need to uninstall FFMPEG again and build a supported version from source.
If your FFMPEG installation didn't get detected, you'll need to tell Audacity where to find it. To do this:
Go to Edit > Preferences > Libraries
Click on the Locate... button.
If a "Success" message appears, Audacity has successfully found FFMPEG.
You can click No as Audacity already knows where to find FFMPEG.
If this message does not appear, proceed with the next steps.
In the "Locate FFMPEG" dialog, click Browse... to locate the libavformat.so.* from the FFMPEG folder you downloaded/installed elsewhere.
Once you've found it, click Open, then OK and OK again to close the preferences.