There are a variety of tools available--many of them open source--to help you turn your data into a visualization, or simply to explore other people's visualizations.
Tableau is a data visualization and analytics package that enables users to connect to a variety of data sources and explore the data in a simplified way. The drag and drop interface make it very easy to visualize and create interactive dashboards without any programming skills.
ArcGIS Desktop includes two applications that are used for mapping and visualization:ArcMap and ArcGIS Pro.
Gephi is a free software for visualizing networks, comprised of "nodes" and "edges". The main website hosts official tutorials and also links to popular community-developed tutorials.