For a complete OSM server for editing etc, what you want is The Rails Port. See this page for details and installation instructions. http://wiki.openstreetmap.org/wiki/The_Rails_Port

Though do you need a complete server and database etc? It would be much easier to just use JOSM, and save your edits to an .osm file on your computer. You can then use that .osm file for rendering maps or whatever else you want to do with the data.