I'm in the lucky position I happen to believe the (nearly universal, or at least overwhelming) consensus in the scientific community about global warming being real. The consensus on the cause of it is admittedly less, but that's not the current discussion.
Had I lived around 1500 I might have believed the same consensus about the sun turning around the earth and have ridiculized Copernicus, like I now ridiculize the non-believers in global warming.
I don't have the time, means, and knowledge to do my own research. But I believe those who do and gather and analyze the data. I'm sure you'll find find those data on the site of the IPCC or other scientific sources (books, journals, sites). Then it's - in principle - easy to disprove those believers by either (a) proving their basic data is wrong, or (b) showing their statistical methods are unsound and misleading. Some poor lone scientist might have tried so, or even done so, but I conclude that hasn't yet caused a noticeable change in the consensus about this being facts.
You might be the one to revolutionize science like Copernicus did!
Those temparature figures are the basic facts. And I feel most SE members don't feel inclined to research them, but still maintain they are untrue.
Most other (real or perceived) changes are indirect. Those include
- retreating glaciers (here precipitation is a factor also, and the relationship between global warming and local precipitation isn't modeled well by current weather models)
- changes in vegetation
- local persistent changes in weather (like the south of Spain becoming dryer)
- changes in timing of bird-migration
- changes in Arctic ice (which of course are also influenced by sea-temperature, snowfall, ocean currents, so that's rather indirect)
The general feeling is that most of this indirect changes are (on the average and on the long run) pointing to an increasing temperature.
http://en.wikipedia.org/wiki/Retreat_of_glaciers_since_1850 has some data on the glaciers. But, as I said, it's only indirectly and not a direct proof of rising temperatures. But surely, it's not a proof of lower temperatures either.