Once you join tabular data to shapefiles in QGIS or have a shapefile with numeric or categorical data, you can symbolize the data using the Style tab in the layer properties:
If you have data that is broken into categories (i.e. male or female, hair color, political party, etc.) you will choose the Categorized option.
The result will look like this:
If you have numeric data you want to symbolize (i.e. total population) choose "Graduated" symbology.
The result will look like this: