Calculations of the age of the universe vary wildly. However, they seem to stay within a range of 10-18 billion years. There are a bunch of ways to calculate the age of the universe. I am currently not sure of the values given by these experiments, so I have none. Here are some:
• Expansion of universe
Measure the hubble constant. This is the rate at which the universe is expanding, and it can be measured by finding out relative velocities of other stars and doing some weird math things to those numbers. With that rate, use some weird physics things to simulate that rate going backwards, until you hit the big bang.
• Age of atomic nuclei
Look at the concentrations of various isotopes in rocks. Use radiological dating to see how old your object is. The universe is at least that old. Also, if you find extremely low quantities of a given isotope, assuming that some of it originally existed, you can use the half-life to get another minimum age.
• Age of oldest stars
Take the oldest white dwarf star you can find (date it radiologically). The star was formed after the universe begun, and therefore the universe is at least as old as that star.
New(ish) news: The WMAP satellite has allowed us to measure the age of the universe to an unparalleled precision: +/- 1%. The answer is 13.7 billion years. This was accomplished by examining the detail in the structure of the microwave background radiation. To me, this seems rather young, as the earth is 4.5 billion years old.