Servant of God - As soon as the cause is opened for consideration the deceased is called "Servant of God. Such as a friend (the Actor Causae) recommends you to be considered to sainthood (typically 5 to 50 years after your death). The Bishop starts investigating and decides that there is a chance they might pass the process. In this investigation, friends, family, coworkers will be interviewed, and your beliefs will be looked into, to be sure you weren't a heretic. Then the research is translated into Latin and sent to Rome.
Venerable - This is what the deceased is called after the Vatican Congregation for the Causes of Saints determines that you did indeed lived a life of heroic virtue (constantly striving to be holy).
Blessed - After the Church establishes one miracle attributed to your intercession, your cause is presented to the Pope to determine your worthiness of being called "Blessed." This is the next-to-last step, and is called "Beatification." If you were martyred, then no miracle is needed, martyrdom counts. A group of Italian doctors (Consulta Medica) will try to find a scientific explanation for the supposed miracle. Some are Catholic, some are not, but all are great doctors. Instances of Incorruptibility, Liquefaction, Odor of Sanctity, Levitation, Bilocation, and Stigmata are also searched for, but those are rare.
Saint - After another miracle is found, then your cause is presented to the Pope again for His judgement. If he determines that the evidence is clear and that contrary reports aren't credible, He may initiate the canonization procedure, which will end in you're recognization as a Saint. This final recognition takes place in the context of a Mass, and a huge tapestry with an image of the deceased is presented for the faithful to look at and admire.