I followed this link and it worked for me…
I can serve tiles locally but running it and by just typing the link like for instance - localhost/osm_tiles/0/0/0.png">http://openlayers.org/en/v3.2.1/examples/localized-openstreetmap.html which is of course an advanced custom tile server. Taking the tutorial I got from switch2osm, is it possible for me to create that same kind of tile server?
This example uses open cycle map tiles. So yes, you can create and use your own rendering styles.
In switch2osm.org tutorial related section is
Stylesheet configuration. You could write mapnik style xml stylesheet or convert it from carto-css project.
This step actually converts carto-css to mapnik xml.
carto project.mml > OSMBright.xml
You could use base OSM style as an example. https://github.com/gravitystorm/openstreetmap-carto
And here you could find how OpenCycleMap style looks like https://github.com/tclavier/mapnik