A trait is a temporally stable, cross-situational individual difference. Currently the most popular approach among personality psychologists for studying traits is the five-factor model, or big five dimensions of personality. The big five were developed by factor analyzing a large number of self- and peer reports on personality-relevant adjectives. The Great Ideas in Personality website covers the big five in depth at the following places: Goldberg's Big Five, and Issues Descriptive and Evaluative.
The big five have been criticized on several grounds. First, they are not universal--only two of the big five have been recovered in Chinese. Second, they represent a "psychology of the stranger"--they are what one might want to know about someone about whom one knew nothing else. Third, they are purely descriptive--they tell us nothing about presumed causation, whether biological or environmental. An alternative trait approach that emphazises biological causation is the PEN model.