How to learn commenting on graphs and tables the right way?
One problem people often have when presenting data in graphs and tables is that they often include data that is not relevant. For talks (formal or informal) I really like the process of starting with an empty graph of just the axes and explaining what the axes are and the limits and what they mean. Sometimes I then like to show idealized data from competing hypotheses so people can know what to expect without the added difficulties associated with understanding real, and potentially noisy, data.

Once people understand what the axes mean, I add data to the plot. Ideally, I start with a single data point and explain exactly what the data point means. I then add additional data points from the same "condition", possibly one at a time if they are discrete or all at once if there is some meaningful function that describes them. Once the first set of data is presented, I add on the second set. Sometimes it is helpful to remove or grey out the first set of data while you are introducing the second set of data so people can focus on just what is new. Once the second set of data is explained, bring back the first set and talk about the relationship between the two sets. This should ideally be moved to a new figure or panel to highlight the differences and similarities you want the listener to focus on.

If there is more "hidden" in figures and tables, that means it is too complicated for a talk. In manuscripts space is at a premium and you often have to have figures that tell multiple stories. In these cases the text still needs to walk you through the figure step-by-step and introduce each piece of information in the order in which you want the reader to look at it.