Basics
Visualizations allow to see the patterns in the data.
Check out that visualization of peak times for sport and leisure. If you want to explore it on your own, here is the original data.
However, we cannot just put the data in the software and expect it to do all the job. Otherwise, we will get something like this: 
The most important thing to remember is that graphs should make a point. Think about the following:
- Hypothesis. What do you want to show?
- Proof. How to emphasize that?
- Explaining. What does the chart show?
Further reading: What Questions to Ask When Creating Charts by Lisa Rost from Datawrapper blog
Form or content?
Both are important for good visualization. Make sure your data is:
- High volume
- Historical
- Consistent
- Clean
- Clear
- Richly segmented
… and you are familiar with it!
When choosing graph, consider how many variables do you have (try to use as little as possible) and what types are they. Do not forget about overall chart purpose and what do you want to show.
Use Data to Viz tool when unsure about graph type.
If you have too many dimensions, refer to the The Art of Effective Visualization of Multi-dimensional Data guide on Medium
Reduce signal-to-noise ratio!