First, establish a time frame - approximately how old is the character and roughly what year would they have been born?
Next, where were they born? Not only does this add depth to the character, but location is an important piece of information in the casting of a horoscope. Astrodienst - Atlas Query Find the Latitude and Longitude of a location.
Third: choose a 'hard' planetary aspect to an outer planet to focus in on as the key component of the chart and the character's personality. This key aspect should be close - within one degree.
For a fictional character, a Square(90°) or Opposition(180°) is far preferable to a Trine(120°) or Sextile(60°). The Square and Opposition are dynamic and energetic, denoting conflicts between the expressions of the planetary themes involved. The Opposition does exactly as is implied - the forces are opposed and contradictory. In the Square, the forces are working at cross-purposes, but there is great energy involved as well for change. The Conjunction is also dynamic, but takes its flavor from the natural compatibility or incompatibility of the planets involved. The Trine and Sextile, on the other hand, are 'soft' aspects. They produce stability and resistance to change, creating an equilibrium that may be resistant to growth as well. Therefore, for the sake of creating a character capable of growth and change (and having interesting problems), making the key aspect in the chart a Square or Opposition seems essential.
The choice of planets in the key aspect is also important. Aspects from Sun, Mercury, Venus and Mars to Saturn, Uranus, Neptune or Pluto carry great energy and the possibility of great internal conflict.
Hard aspects to Uranus, Neptune and Pluto imply the character will have difficulties with the status quo.
The aspecting planet is also important as it determines which energies will be used (or have difficulty with) the energies of the outer planets.
Aspects between Uranus, Neptune and Pluto are generational - the planets travel so slowly that aspects between them effect entire populations, thus giving rise to the similarity of issues affecting a cohort (people of the same age) and differences between one cohort and another. For example: Uranus Squared Pluto off and on from May 1931 to Feb 1934. This aspect indicates a group of people living in times of drastic upheaval, war, revolution, violent and unpredictable change. (The Depression, WWII, the Cold War, Korean War, etc.) Uranus Conjuncted Pluto off and on from October 1963 to July 1968. This cohort is now in their mid to late 50's - the group most strongly allied with the computer/communications revolution with the potential of regenerating outmoded social institutions or overthrowing them altogether. While these aspects usually do not have strong bearing on the individual (unless one of the faster moving planets is also aspecting them), it does give certain insights into the psychology of that generational group.
Note: for those writing characters that have been (or will be) portrayed on stage or screen - avoid assuming the actor's horoscope has any bearing on that of the fictional character he or she is portraying. The actor's horoscope belongs to an actor, not a secret agent, doctor, or lawyer. While there may be many points of congruency between the actor's abilities and personality and those of the fictional character, keep in mind that the character has been brought to life by the combined efforts of the writer, director, other members of the film crew, and the actor. That said, it also seems logical to add something of the actor to the fictional character's horoscope. A recommended method is to use the actor's sun sign or ascendant as the character's ascendant to represent the actor's contribution to the portrayal of the character.
Some books on the subject: Western and Celtic Astrology
Some other sites: Astrology Links