One indication of the size and age of the universe comes from analyzing the light emitted by distant galaxies. When astronomers look at the spectra of their light, they can classify these galaxies into two primary groups:
BLUESHIFTED objects are moving toward us have absorption lines in their spectra shifted toward the shorter, bluer wavelengths of light;
REDSHIFTED objects, on the other hand, are moving away from us, and have spectra shifted toward longer wavelength and redder light.
Diagrams. Red shift and Blue shift. Notice the shorter wavelengths of the blue -- when objects are coming towards us -- and longer ones towards the red -- when objects are moving away. Original diagrams by The Online Planetarium Show.
The amount of a galaxy's red-shift tells astronomers how fast the galaxy is moving away from us. The farther away a galaxy is, the faster it's moving away from us. That's Hubble's Law. If it is known how far away the galaxy is, scientists can calculate the rate the universe is expanding between us and the object. Using the expansion rate we can determine how long it has been since the universe was crunched into a single point at the moment of the Big Bang.
This would be fairly straightforward except that a galaxy's motion is not just based on the expansion of space. Gravity pulls on the galaxies -- from other nearby galaxies and from clusters of galaxies. It's also extremely difficult to measure the distance to galaxies outside the gravitational influence of our own Milky Way. That's why astronomers are using the Hubble Space Telescope to help measure and observe.