The Open Data Institute in the UK offers "data skills courses to balance technical with non-technical skills to ensure that people can make an impact with data, and help ensure the best social and economic outcomes for everyone." We too can use their Data Skills Framework to plan our studies.
The School of Data Methodology is a sequenced approach to working with data from beginning to end. Once you better understand the data cycle and stakeholders, breaking down the process into steps helps to build confidence in your work.

As an excellent introduction and set of warm up exercises, we use the DataBasic online tools and methodology to explore simple datasets as a group.
Where to get more experience. Building a toolbox for data wrangling. Finding questions to ask. How to interpet, verify and reuse a data source properly.
Ihr Kinderlein, warum kommet ihr nicht? (Republik) is an excellent overview of some of the ways that people are misled by visualizations, from some of Switzerland's leading online data journalists.
Information is Beautiful showcases the most talented and most accurate work in data visualization around the world. This chart by Fabrice Sabatier is an overview of how the discipline has developed over the last centuries.
seeing-theory (Brown) is a highly recommended set of online tutorials that introduce you to the basics of statistics in a fun, interactive way. Must see!