When people talk about human influences on the global climate, they tend to think that there is much less certainty in the conclusions than actually exists. In fact while the models have a lot of approximations and simplifications, they really do an excellent job simulating the global climate history. You want proof? Behold NASA's really pretty graph (click for a larger version or click here to read the full article):
The dashed line is recorded average global temperature anomaly, which are uncertain to maybe 0.3 degrees C but become particularly reliable after about 1970 when space-based measurements became available. The red line is the average of several global climate models including human influences and the blue line is the average of those same models without human influences. You'll note that almost all of the observed warming does not occur in the models without human influence. All I have to say is WA-BAM! Physics Works!
One other interesting thing to note: the two largest natural influences on climate are volcanoes (labeled and with vertical grey lines) and the El Nino cycle. So it's not that the climate isn't strongly influenced by natural events, it's just that these events don't tend to produce a consistent heating or cooling effect. Humanity, on the other hand, is consistently heating the planet and shows no signs of stopping.