Human-induced climate change has expressed itself in elevated concentrations of CO2 in the atmosphere. Elevated CO2 is a consequence of releasing carbon in the atmosphere through burning fossil fuel like coal and petrol. Among multiple evidences for such change, glacial ice cores represent the most convincing indication of human-induced elevated CO2 levels. As glacial ice forms every year it trap atmospheric air in the form of bubbles. Extracted from drill holes, glacial ice cores can be accurately dated to the recent time line (back to several thousand years). Extracted air bubbles are analyzed for concentration of gases and isotopic composition of the gases. This graph below copied from "Stable Isotope Geochemistry" by Hoefs represents the most convincing evidence for human-induced climate change.
Clear increase in CO2 concentration (plot a) starting at about 1850 marks the bloom of the industrial era. Plot B shows the carbon isotopic composition (δ13C, ‰; delta carbon thirteen) of CO2 from the atmosphere. Starting from industrial era, it becomes more negative, meaning CO2 molecules in the atmosphere are increasingly depleted in the heavier isotope of carbon - 13C - with respect to the lighter carbon, 12C. Organic matter, like coal, is extremely "light" carbon, means it is depleted in heavy carbon 13C. Burning such "light" source of carbon makes CO2 in the atmosphere "light" as well. Just for clarification, I include here a diagram from the same book on isotopic composition of all carbon sources known to Earth. It shows that organic matter (such as fossil fuel) is the source of isotopically "light" carbon.
It was pointed out that the isotopic composition of CO2 from volcanoes should be shown too since volcanic emanations contribute to the level of atmospheric CO2. Valid point. The δ13C from volcanoes is almost identical to the δ13C of the air. See attached diagram.
The image is taken from a Pennsylvania State University website