To improve your graph skills, 3 things you can do below:
1) First, to have a good understanding of the different type of charts. Understand which chart is typically used for which purpose. E.g. stacked bar chart for component, column or bar chart for time series or frequency, dots for correlation, etc. To begin with, you can read the book "Say it with charts". PM me if you need more info.
2) Second, practice reading by looking into MBB articles they publish on their websites. Look for the charts. Cover up the title or the take-away, read the graph and try to see what is the key message you get out from the graph, then compare with the key message the authors are putting forward. See where is the gap, and where you miss some key insights.
3) Plus, you can further practice by drawing your own charts. Use some data set from your work or school, think about if you were to put those data into charts how would you do it, what is the key message you want to get across. Then present your charts to someone else, and see if the message is coming out clearly, or if there a better way to present your charts.
Hope it helps,