First create the PostgreSQL database:
createdb yourdatabase
Then add plpgsql support to that database:
createlang plpgsql yourdatabase
Then you need to import these two SQL files into that database to set up the PostGIS functions:
psql -d yourdatabase -f /usr/share/postgresql/8.4/contrib/postgis-1.5/postgis.sql
psql -d yourdatabase -f /usr/share/postgresql/8.4/contrib/postgis-1.5/spatial_ref_sys.sql
That's it!
QGIS has a nice plugin tool for pushing shapefiles into postgis enabled postgresql databases called SPIT(Shapefile to Postgresql Import Tool