To create a new empty database, run as postgres-user:
createdb [yourdatabase]
Connect to the database with a psql-session:
psql -d [yourdatabase]
In the psql-session run:
CREATE EXTENSION postgis;
CREATE EXTENSION postgis_topology;
to create the neccesary geospatial extensions. Once this is done, the database is a geospatially enabled database and it is ready to use.