Original instructions:
1. Get up-to-date data (e.g. from appstream.debian.org/data/: Navigate to the Debian suite you are running (e.g. "unstable") and download the icon tarballs and *.yml.gz files for the archive components (main, contrib, non-free) you want data for.)
2. Copy the *.yml.gz files to /var/cache/app-info/yaml (you may rename them, e.g. to "unstable-main_amd64.yml.gz") and extract the 64x64 icon tarball to /var/cache/app-info/icons/%{suite}-%{acomponent}/64x64, where "suite" is the archive suite the icons are from (e.g. "unstable") and "acomponent" is the archive component (e.g. "main").
3. Run appstreamcli refresh-cache --force (needed for SCs which use the Xapian cache for fulltext search)
Repackaged instructions:
Download linked file and decompress.
From uncompressed directory, copy app-info to /var/cache
sudo cp -R app-info /var/cache
Rebuild appstream cache
sudo appstreamcli refresh-cache --force