There are multiple steps that are taken for a priest to be named a bishop.
Stage 1. Every bishop may submit to his archbishop the names of priests he thinks would make good bishops. Following a review and discussion of the candidates at the regular province meeting of the bishops, a vote is taken on whom to recommend. The vote tally and minutes of the meeting are forwarded by the archbishop to the apostolic nuncio in Washington, D.C. The list is also submitted to the United States Conference of Catholic Bishops (USCCB).
Stage 2. The apostolic nuncio conducts his own investigation into the suitability of the candidates, which he interprets for the Congregation of Bishops. He consults with the bishops about the needs of the diocese, with the leadership of the USCCB, and with a few references who know the top candidates personally. The nuncio prepares a report and then lists his top choices alphabetically (the terna) with his preference noted; this is forwarded to the Congregation. Great weight is given to the nuncio's recommendations, but they are not necessarily always followed.
Stage 3. If the appointment involves a bishop who is being promoted or transferred, it may be handled by the prefect and staff. If the appointment is of a priest to the episcopacy, the full Congregation is ordinarily involved. A cardinal relator summarizes the documentation and makes a report to the full Congregation, who discuss the appointment before voting. The Congregation may follow the recommendation of the nuncio, choose another of the candidates on the terna, or even ask that another terna be prepared.
Stage 4. At a private audience with the Pope, the prefect presents the recommendations of the Congregation. The pope can do one of four things: He may agree with the Congregation’s proposal; he may choose another candidate on the list; he may ask for a new terna; or he can choose his own candidate. The Pope then informs the Congregation of his decision. The Congregation notifies the nuncio, who contacts the candidate. If the candidate accepts, the Vatican is notified and a date set for the announcement. It can take six to eight months to appoint a new bishop to a vacancy. According to Church law, bishops-elect are to be ordained within three months of their nomination.