This page shows some examples of what Graph extension can produce. Graphs use Vega grammar (documentation) as underlying technology. Vega team is working on other tools to make Graphs easier to use. For interactive graphs this tutorial will explain building graphs step by step. For other graph ideas, see Vega examples.
The easiest way to use graphs is via pre-built templates such as the Graph:Chart (available on many Wikipedias), or more specialized PieChart. Graph:Chart supports many common graph types such as line, area, and pie charts:
Editing JSON by hand is fiddly and prone to error. so you should use a JSON checker such as JSONLint or a JSON editor such as the Vega Live Editor to edit JSON before you copy and paste it into the wiki page. If the <graph> tag's data is directly embedded in the page such as the example above, then if you use VisualEditor to edit the page you can directly edit graph data.