If you take the ticks of a clock, and have two people observing them, one of them standing still and the other in motion, then the person who is in motion, will view the time in-between the ticks as longer. T0= time measured by a stationary observer. T= the time measured by the observer in motion. V= the velocity of the person in motion. The link below shows the formula.
Another example of time dilation would be having a light clock. For a stationary person, the light would apear to be going straight up and straight down. However, for a person who is in motion, the light would apear to be traveling a much greater distance, like the image below.
http://www.pa.msu.edu/courses/2000spring/PHY232/lectures/relativity/dilation.html
http://casa.colorado.edu/~ajsh/sr/time.html
http://mindblowingphysics.pbwiki.com/f/PA.MSU.EDU.jpg?sz=400