I'd like to set up my own tile server but I'm very new to it all and do not know what to do next. I followed the guide Switch2OSM on how to install OSM locally. Surprisingly I successfully got through it after a few wrenches thrown in. Now I have no idea how to display my map in a locally hosted web page. I saw the tutorial on leaflet through Switch2OSM but its not for a local server and is very uninformative to a beginner. Any help on where to go next would be great.
I found some hints via https://help.osm.org
... maybe the magic word is "localhost"?
Give us more details where you get stuck.
See the Quick Start Guide. There you will create a
L.tileLayer object where you can just add the URL to your very own tileserver, probably starting with http:/localhost/ or the address of your webserver. That's all.