Introduction

There are many faces of the science of Global Climate Destabilization (GCD) — many fields of study are involved, such as

Climatology, Meteorology, and Atmospheric Physics
Oceanography, Geology, Glaciology
Ecology and Biology
Forestry and Agriculture
Mathematics and Statistics

All these fields come together and work on a huge playground, called Planet Earth. Each is working at different scales: some are doing climate modeling for the whole earth, while others may be working in one small region of one small country (e.g. a herpetologist studying a frog in the Monteverde Cloud Forest of Costa Rica). Some study data from millions of years (e.g. ice cores, ocean bed), whereas others are lucky to have a few years of spotty data. In any event, all these scientists come together to try to get a handle on the big picture:

(from the National Academy of Science)

There is, however, one thing upon which nearly all scientists agree: the cause of the dramatic climate change underway is human activity (and, in particular, what I call the "carbon crisis"):

the burning of fossil fuels, which, together with the "Greenhouse Effect", cause warming;
landscape changes such as widespread deforestation (and the consequent loss of trees, nature's carbon sequesterors); and even activities such as
the production of cement (which liberates carbon from limestone).

The impacts are many, and diverse. For example, many people are not aware that carbon is also being absorbed into the ocean on a vast scale: more carbon is going into the ocean than into the atmosphere. In some sense, that's good news: the greenhouse effect would be greater if that carbon had gone into the atmosphere, to warm it; however, the carbon in the ocean is causing its waters to become increasingly more acidic, which is resulting in the direct destruction of many sea creatures' shells. Furthermore, the waters of the ocean are warming, and between the two of these effects, our coral reefs around the world are threatened with destruction.

The ocean's waters are also rising, in consequence of both the expansion of water when heated, and the melt of the land-based ice in glaciers, particularly in Greenland and Antarctica. Scientists expect at least one meter of sea-level rise by the end of THIS CENTURY. That's pretty astonishing. If you've ever been on the beach at an ocean, imagine the ocean a meter higher: what would have been impacted? Imagine storms with more energy, crashing much higher up the beach — and you have some idea of what we expect in the next 85 years or so.

Agriculture, too, will suffer because of climate change. Although plants do use CO2 as a fertilizer of sorts, too much of anything is a bad thing, and CO2 and higher heat together are likely to reduce the capacity of farmers to produce the food that we rely on. That, in conjunction with projections of higher populations in the decades ahead, seems to be a recipe for disaster:

Scientists studying climate change are faced with the daunting task of trying to understand what is going on in many different sciences, only one or two of which one will have generally mastered. That means that one must be a jack of many trades to engage in the research and study of GCD. Furthermore, there are many timescales, as indicated above.

Fortunately there are many valuable resources. In terms of a big (some might say "vast") picture of the science, one can hardly do better than the IPCC (Intergovernmental Panel on Climate Change) reports, which have now been issued five times since 1990:

IPCC 2014
IPCC 2007 (the IPCC received the Nobel Prize for this report)
IPCC 2001
IPCC 1995
IPCC 1990

These reports are striking, especially given that they are consensus documents, and actually tend to be on the conservative side in terms of predictions.

Some general resources:

Key Science Basics of Climate Change
Climate Change: An Information Statement of the American Meteorological Society (2012)
Geoengineering: An Information Statement of the American Meteorological Society (2013)
12 Graphics That Contain Everything You Need to Know about Climate Change (David Biello | January 31, 2014 — local copy)
Climate Change Science Compendium 2009 (United Nations Environment Programme)
A great reference to the historical literature is The Warming Papers, edited by David Archer and Raymond Pierrehumbert. This is a collection of the most important papers underpinning the science of climate change as of 2011, the year of its publication.
How to Talk to a Climate Skeptic: Responses to the most common skeptical arguments on global warming
What is Science Literacy?
Teaching about Climate from NOAA
Teaching about Climate with the New York Times

Science Breakdown (is that a fiddle tune?)

Climatology, Meteorology, and Atmospheric Physics

What is the average global temperature now?
The Discovery of Global Warming from the American Institute of Physics. A great hyperlinked overview of many aspects of global warming and climate change.
Climate Wizard: provides projections of future climate