How to tell if a single day of weather is an anomaly or due to climate change?
I am interested in understanding how to tell if a single day of 'abnormal' weather is due to climate change or not.


You can't. The day-to-day, locale-to-locale variations in weather are huge compared to the changes that occur from year-to-year and decade-to-decade, averaged over the surface of the Earth. Most of those climatological variations are periodic in nature (e.g., El Niño Southern Oscillation, North Atlantic Oscillation; note the "oscillation" in the names). Climate change is the small but steady secular change in climate.

Another way to look at it: Even the most pessimistic of projections is for a 4°C increase over the course of a hundred years. That corresponds to 0.04°C change per year. Weather can bring about a 4°C change over the course of a few minutes. Any one weather event can be attributed to the noisy, flukey nature of weather. Climate change begins to become apparent when one looks at weather events that occur all over the face of the Earth, and over the course of several decades.