Evidence leads to predictions
Evidence for climate change comes from scientists all over the world. They collect data such as temperatures in remote locations, and the areas covered by summer and winter ice at the poles. These data are then entered into computers and used to generate models of what is likely to happen, given what has happened in the past. See How Computers Model Climate Change by Dr Vicky Pope at the UK Met Office's Hadley Centre for Climate Change for more information.
The Hadley Centre's predictions rely on projections which take into account population growth, energy use, economics, technological developments, and so forth. For more tables and graphs, see the slides from the Hadley Centre climate change brochure on 'Climate change and the greenhouse effect'
Some activities are more complex to model than others, in particular the concept of feedback where the outcome of a change affects the change itself. They haven’t yet been incorporated into the models used to inform the IPCC reports, but scientists are talking of 'tipping points' such as the physical collapse of the Greenland Ice sheet and a potential shut-down of the Atlantic currents bringing warm water to the UK.