how can you recognize possible associations and trends between two categories in categorical data
I would say that the easiest way to recognize possible trends between two data sets is to graph the data on an x/y chart. You can do it by hand and draw out the graph, or you could use a spreadsheet program like Google Sheets or Microsoft Excel. Both will allow you to input numerical data, click the chart icon, and generate multiple graph types (line, area, bar, column, etc.).
What the graph will allow you to clearly see is any supposed relationship. For example if the relationship is directly proportional, then the line on the graph will show positive slope. Something like foot size and shoe size both increase together. That's an overly simplistic example, but the chart might be able to show you a correlation between height and shoe size or whatever.
If the trend is inverse, then the line will show a negative slope. This would be something like Boyle's gas law. As the volume of a gas increases, it's pressure decreases. If you graphed that, then the line would go down as it went from left to right along the x-axis.
The graph would also be able to show you an exponential relationship too. That kind of data plot would have a line that gets steeper as it moves along the x-axis. Lastly, the data plotting on a graph would clearly show out lying data and possibly no relationship at all.