cycle map

how do you save tracks as cycle paths, routes, mtn bike trails and have them show up in the osm cyclemap layer?

I am assuming you have created a gpx trace from using your garmin or similar device or smart phone app and now want to add it to the openstreetmap and see it displayed on osm cycle layer.
You need to display the gpx trace using one of the osm editors - id, potlatch2 or josm - and then use the tools in the editor plus satellite imagery if available to add a way following the gpx trace you loaded. You the add appropriate tags to the new way you have created and save or upload your changes to the osm database.
After a while the new way, a track or footway or path or whatever you have created, will eventually be rendered and show on the osm. The standard layer is usually quite quick to display after refreshing your browser. The cycle layer is updated about once per week i think.