Using psql how do I list extensions installed in a database?

In psql that would be

\dx

See the manual of psql for details.

Doing it in plain SQL it would be a select on pg_extension:

SELECT * 
FROM pg_extension;

Additionally if you want to know which extensions are available on your server: SELECT * FROM pg_available_extensions.

See pg_available_extensions and pg_available_extension_versions.