There are several ways to determine from data that humans are likely to be responsible for the warming trend. 

One basic approach is to conduct a time series analysis on temperature or carbon dioxide data that has been collected at weather stations and through ice core samples. Two models can be fit to the data: the first considers only the last 60-100 years of accumulated data, while the second considers all other historical data which predates human industrialization. A hypothesis test can be used to show that these two models represent significantly different data sources, or in other words, the period of human industrialization corresponds with an unusual warming trend in Earth's history. 

While correlation need not imply causation, such a large quantity of analyses have been conducted around similar hypotheses and other data sources that the alternative point of view (the warming trend is due to naturally occurring phenomena) has been deemed unlikely by the vast majority of climate researchers.
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