Regions - Cultural and Sport

First of all, OSM does not have the concept of layers. Some maps might place data from the OSM database (or other databases) into layers. So I see the following solutions for you:

1. The data is already in OSM and you just need a map to render the data. A combination of Overpass and Leaflet could be used here
2. The data is not yet in OSM (likely). You can consult the community in your country to add this data with proper tags. Then you can do 1 (if they want/can to add the data)
3. You have this data available in some format (e.g. shapefiles). You can use e.g. Leaflet to put the data in a layer of a map that you create yourself (programming required)
4. You have the data available and use e.g. http://umap.openstreetmap.fr to create a map (no programming required)

Leaflet is a Javascript framework to display maps with all kinds of markers, layers, etc. OpenLayers is an alternative.