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Volcanoes produce carbon 13, and this isotope is measurable. It is not a significant part of the increase of carbon dioxide in the atmosphere.
Wild fires produce a know proportion of carbon 14, because the plants that burn - are younger than 50,000 years. Carbon 14 is radioactive, and it has a known rate of decay - and is how we do carbon dating.
Burning fossil fuels ONLY produces carbon 12 - because the plants that became the coal and oil and natural gas - is much older than 50,000 years. So, when the proportion of carbon 12 is such that it could ONLY have come from fossil fuels - this is one way that we know that what we are doing is causing climate change.
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