First, look for a file with geographical information at the geographical level do you need (country, regions, provinces, counties, etc.). One of the most common are shapefiles (actually each shapefile is a set of files with the same name but different extensions). You have to google it. Once you have your "shapefile", the easiest way to map is Geoda. If you are confident with R, then you have many alternatives depending on the package you use to read the shapefile ("sp" vs "sf"). Then you can use ggplot or tmap for mapping.
I personally think QGIS will be the most suitable option for you to perform the mapping task for you. Arc GIS is good but its a paid option, although you can crack the software but its a hectic process to follow. Other than that its a bit clumsy to operate for any new user. On the other hand QGIS is a open source tool and certainly much easier to use than arc GIS .
Mapping is such a broad term and involves depiction of data in a visual manner. This to me suggests that you have to first assess the type of data you want to depict then determine the appropriate mapping method and tool to use. The suggestions given are good but i think your first step is to have a clear understanding of what to depict then investigate the tools. Hope this helps.
Thank you Hasibul Hasan , Javier Beltrán , Joaquín Duque Lazo , Obaidur Rahman , Ebere Ekemezie , Oyedotun Victor Tunde , Ahmad Rajabi , Bidhan Bhuson Roy these are wonderful tips and i'm grateful. I have Qgis and will learn to use it. You're right Julian Simela . I need to have an understanding of the data and how to use it.