How Do We Know the Age of the Universe?

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What kinds of tools do astronomers use to calculate the age of the universe, and how can they determine the speed of its expansion?

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Sources:

https://www.nasa.gov/mission_pages/hu...
https://www.wolframalpha.com/input/?i...
https://www.nobelprize.org/nobel_priz... http://articles.adsabs.harvard.edu/cg...
http://articles.adsabs.harvard.edu/cg...
https://www.cfa.harvard.edu/~dfabrica...
http://www.annualreviews.org/doi/pdf/...

Images:

http://www.thinkstockphotos.com/image...
https://en.wikipedia.org/wiki/File:Da...
https://www.nasa.gov/mission_pages/hu...
https://en.wikipedia.org/wiki/File:As...
https://commons.wikimedia.org/wiki/Fi...
http://www.esa.int/spaceinimages/Imag...