What has contributed to the increased amount of greenhouse gases in the atmosphere today?
It depends on which greenhouse gas you are referring too.
The most talked about greenhouse gas is Carbon Dioxide. The things that are increasing the amount of it today are the burning of fossil fuels (coal and gas for example, are carbon based and release carbon dioxide when burned), and the depletion of forests as plants are what take carbon dioxide out of the atmosphere.
The next greenhouse gas that is increasing (although not nearly as quickly) is methane. It is released from rotting material and as a byproduct of digestion. This is increasing in a couple of ways. The diet that most meat producing animals receive is not the best diet to reduce the amount of methane produced (yes I am talking about cow farts). Furthermore the sheer number of farm animals is quite high and therefore the amount of methane they produce is high.
The other thing that increases methane is the thawing of permafrost. This frozen material does not rot (cause it's frozen) so when it thaws and begins to rot it releases methane. Permafrost is thawing due to global warming which is due to increased greenhouse effect, so this is a feedback loop that is difficult to stop.