Map editing is quite an easy job to be done on Open Street Map. Map editing is of two types here:-
In Online map editing, we use ID editor. It is easy to use. It contains Edit Feature Pannel, some tools and Map Pannel. Using ID, you can add points, draw lines and shapes as well. You set accessibility information and can also add notes, Wikimedia links etc.
In the other case, we can use JSOM which is far more configurable editor than ID.
You can learn both from the following links easily. This website provides really good beginners guide for both including their comparison.