Evidence in support of warming:
Measurements of surface stations, ocean buoys, balloons & satellites. Change in seasonal arrival time and the movement of plants and animals. Isotope analysis of ice cores, deep sea sediment cores. Thermal analysis of boreholes. Measurement of tree rings.
Evidence against warming:
Claims that 'Urban Heat Islands' are skewing the temperature record. There aren't enough surface stations. 1934 was one of America's hottest years. It's all a natural cycle.
Evidence for ice caps melting:
I assume you mean melting faster than they're being replenished, since even at -10C there is a high probability of some ice melting from thermal agitation!
Evidence in favour: Observations of glaciers on mountains, Greenland & the Antarctic Peninsula. Gravity based measurements from the GRACE satellite. Altimetry readings from aircraft. Observation of the Arctic ice cap by satellite. Evidence for historical comparison are things like cyclothems (alternating marine/non marine sediment near shorelines) and isotopic analysis of deep sea sediment cores and foraminifera.
Evidence against: the above suggests East Antarctica is probably growing. This is consistent with climate models, that predict the increased snowfall will outweigh the increased melt (since Antarctica is so cold anyway). Antarctic sea ice may be growing. Greenland, continental glaciers, the Arctic sea ice, West Antarctica and the Antarctic Peninsula appear to be shrinking significantly.
Further evidence is 'it's all a natural cycle', Greenland and the Alps had less ice on in the past, people sailed into the arctic.
The globe warms and cools all the time:
That's pretty much irrefutable. All the above (tree rings, bore holes, isotopes) plus historical records. The current warming seems to be faster and higher than anything in the last 2,000 years, it's pretty much opposite of what we'd expect from 'natural cycles' and it can currently only be explained by human caused global warming, however.
Scientists only have info on temps for the last 100 years or so:
Worldwide that's true. Satellites only for 30 years. However, even with thermometers and satellites are only estimations. If you have a thermometer that gives you 21.34C, then it's an estimate to +/-0.01C accuracy. Beyond this, we have paleoclimate records that are less accurate, but far from useless - their results are compared with the thermometer record and they generally prove to be pretty good.
