A good answer there from Astronomy 101 but a slight error regarding the way the atmosphere warms. It's not so much that greenhouse gases destroy the ozone layer, it's that they have the ability to retain heat.
Climate change (and global warming) is caused by greenhouse gases in the atmosphere, these gases include carbon dioxide, methane and nitrous oxide. Greenhouse gases absorb some of the heat which is emitted outwards from the Earth, and the more of these gases there are the more heat is retained in the atmosphere.
The biggest cause is nature itself but I guess your question relates to the way human are causing climate change.
Our modern way of live produces a lot of greenhouse gases and one of the main sources is the burning of fossil fuels (natural gas, oil, coal). These fuels have a lot of carbon in them and when they're burned they react with oxygen in the atmosphere and make carbon dioxide - a greenhouse gas.
Cutting down trees for lumber or to create open spaces for fields and buildings is another contributor. Trees absorb carbon dioxide from the atmosphere when they're growing and when they're cut down and burned or left to rot they re-release the carbon dioxide.
Fertilisers that farmers use on their fields contain different chemicals and one of these produces a lot of nitrous oxide which is another greenhouse gas.
Lots of different industries and industrial processes such as making cement, making steel, making cars etc also produce lots of these greenhouse gases.
And much of our waste produces methane. As rubbish decays in landfill sites it gives of methane gas and so does sewage waste.
All these things make the greenhouse gases that get into the atmopshere and trap heat.
Let me know if you need more examples and I can add some more.