How much of the current global warming is due to human influence?
Firstly it is worth demonstrating that 97% of climate scientists agree that climate-warming trends over the past century are very likely due to human activities.


  W. R. L. Anderegg, “Expert Credibility in Climate Change,” Proceedings
  of the National Academy of Sciences Vol. 107 No. 27, 12107-12109 (21
  June 2010); DOI: 10.1073/pnas.1003187107.
  
  P. T. Doran &amp; M. K. Zimmerman, "Examining the Scientific Consensus on
  Climate Change," Eos Transactions American Geophysical Union Vol. 90
  Issue 3 (2009), 22; DOI: 10.1029/2009EO030002.
  
  N. Oreskes, “Beyond the Ivory Tower: The Scientific Consensus on
  Climate Change,” Science Vol. 306 no. 5702, p. 1686 (3 December 2004);
  DOI: 10.1126/science.1103618.


But what percentage of the increase is attributed to humans?  Probably almost of all of it.

The scientist Gavin Schmidt from NASA was asked this question on realclimate.org

His response was as follows:


  Over the last 40 or so years, natural drivers would have caused
  cooling, and so the warming there has been (and some) is caused by a
  combination of human drivers and some degree of internal variability.
  I would judge the maximum amplitude of the internal variability to be
  roughly 0.1 deg C over that time period, and so given the warming of
  ~0.5 deg C, I'd say somewhere between 80 to 120% of the warming.
  Slightly larger range if you want a large range for the internal
  stuff. [emphasis added]


The rapid increase in the human-driven component of the forcing are increasingly dwarfing the small, slow natural forcings, rendering them increasingly irrelevant.