How to deal with the Open Street Map?

Question

Java

I can't figure out how to put a mark on an object (or several objects on one map) on the OSM map, sign a name (or some other information) on it in the "cloud", and draw a path from the object to something !!!
Everything is very simple on Yandex and Google, BUT I need to do the same on OSM!
It just needs to be something like this - the map is at the bottom of the page

Answer 1

So there is just a link to this library on the map - leafletjs.com