The easiest way is to set up GeoServer as part of the OpenGeoSuite. The OpenGeoSuite sets up PostGIS and GeoServer and another application called GeoExplorer, which is a web-app that sorts out authentication and editing of spatial data, as well as simple styling.
That said, you can't just 'make a map.' You need to set up multiple tables, all with an appropriate schema, to hold all your different layers. That stuff takes experience, or will require you to iterate over time in order to get it right.
You could set it up in a Desktop environment first, use QGIS for that. Edit data in PostGIS for best practice, or use SHP files for ease of use.