One package manager, one command
For 99% of you, installing FFmpeg is a one-liner through your OS's package manager. The only people who need to compile from source are those chasing a specific patent-encumbered codec, an unreleased filter from git master, or an enterprise-locked CI image. We'll cover the sane path first.
macOS — Homebrew
On Apple Silicon and Intel Macs, Homebrew's ffmpeg formula bundles the most useful libraries (libx264, libx265, libsvtav1, libvpx, libdav1d, libvmaf, opus, lame, openssl, sdl2) and enables VideoToolbox/AudioToolbox for hardware encode/decode. That's what you want.
Linux — distro package, then upgrade if needed
Ubuntu/Debian: sudo apt install ffmpeg. Arch/Manjaro: sudo pacman -S ffmpeg. Fedora: sudo dnf install ffmpeg-free (or the RPM Fusion ffmpeg for full codecs). The downside: distro packages are often a major version behind. If you need 8.x today on a Ubuntu 24.04 box, use the official static builds from johnvansickle.com or the jellyfin-ffmpeg packages.
Windows
Use winget install Gyan.FFmpeg or grab a static build from gyan.dev. Avoid hand-installing into C:\\ and editing PATH unless you enjoy that.