Evidence shows that the amount of carbon dioxide in the atmosphere has risen sharply since the Industrial Revolution, and so has the average global temperature. Over the same period, people have burned much more fossil fuel. When the data are plotted on a graph, the rise in carbon dioxide closely matches the rise in fossil fuel use. This is a correlation, and a link like this is evidence for human causes of climate change, but a correlation alone does not prove one thing causes the other (causation).
Burning fossil fuels is not the only anthropogenic (human) cause. Deforestation removes trees that take in carbon dioxide, and farming releases methane from cattle and rice paddies. Landfill sites also release methane as waste rots.
There are uncertainties in the evidence. Climate is very complex, so predictions come from computer models that rely on assumptions. Data from the past, such as from ice cores or tree rings, is indirect and less precise than modern measurements. Natural causes such as volcanic eruptions and changes in the Sun's output also affect climate. Some reports in the media are biased or are not checked by other scientists. Good evidence is repeatable and has been checked by other scientists, which is called peer review.