The ‘fingerprint’ of human action on climate can be found from a number of features of global change that point towards our actions driving the changes:

But another way we can determine the cause of a change is by a so-called attribution study. For this we need:

1. observations (e.g. temperature, precipitation, sea level)
2. history of the potential system forcings (e.g. greenhouse gases, solar activity, volcanism)
3. a model connecting 1 and 2 (can be simple or a complex numerical representation of real world physics)
4. estimate of magnitude of internal variability of the system (the “noise”)

By running the model with the different possible forcing factors as inputs, and then comparing the model output to the observations we can see to which forcing we can most reasonably attribute the observations. This is nicely illustrated in this figure from the IPCC Special Report on Ocean and Cryopshere in a Changing Climate

You can explore a very nice animation of attribution of recent global temperature evolution here: https://www.bloomberg.com/graphics/2015-whats-warming-the-world/