How to properly monitor the number of PostgreSQL database connections?
Its better to use Workload monitoring tools like pgbadger for checking database connections and overall load. It will help you understand which users are connecting for how much time and what queries are being fired by them. For information on installing and configuring pgbadger, refer this page.

If you just want to check the number of active connections, you can use
 select count(*) from pg_stat_activity where state='active'