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.

This SQL query gives output similar to \dx:

SELECT e.extname AS "Name", e.extversion AS "Version", n.nspname AS "Schema", c.description AS "Description" 
FROM pg_catalog.pg_extension e 
LEFT JOIN pg_catalog.pg_namespace n ON n.oid = e.extnamespace 
LEFT JOIN pg_catalog.pg_description c ON c.objoid = e.oid AND c.classoid = 'pg_catalog.pg_extension'::pg_catalog.regclass 
ORDER BY 1;

Thanks to https://blog.dbi-services.com/listing-the-extensions-available-in-postgresql/