While pew-cushion pundits speculate on who the next archbishop of Washington will be, the actual process of choosing a successor to Cardinal William W. Baum will take several months and involve a substantial number of Washington-area Catholics.

The central figure in the search for a successor to Baum, who was named to a high Vatican post this week, is the genial Belgian-born Apostolic Delegate, Archbishop Jean Jabot, the Vatican's man in this country.

Jardot and his staff are diplomatically noncommittal when asked who is under consideration, what kind of a man is being sought, or even how long the selection process will take. The actual process was spelled out eight years ago at the direction of Pope Paul VI.

Under these guidelines, before Baum packs up and heads for Rome, he is obligated to provide Jadot with "a full and careful report on the condition and needs of the diocese."

Similar information will be sought from official clergy and lay groups in the diocese, such as the senate of priests and the pastoral council.

In addition, a substantial number of Catholics throughout the diocese will receive a questionnaire in the mail from Jadot soliciting their views on the kind of leadership the archdiocese needs and inviting them to nominate candidates.

Jadot also will seek suggestions from Baum and from the president of the National Conference of Catholic Bishops, Archbishop John Quinn, of San Francisco.

From this mass of information, Jadot and his staff will select the three men he considers best qualified and forward their names to Pope John Paul II for his choice.

Although the Washington archbishop has many problems, the post is considered a plum in the American church; the competition for it will be limited to the real comers of church leadership. The job not only reflects the excitement and power of the nation's capital, but Washington also houses the national offices of the church hierarchy. Best of all for an ambitious churchman, the man who comes here is almost certain to be named a cardinal.

The new archbishop of Washington can be an archbishop moved laterally from another archdiocese, a bishop promoted from a diocese, or even a man plucked from the rank and file of the priesthood. The latter is considered highly unlikely. Still, Archbishop Rembert G. Weakland of Milwaukee made such a jump three years ago, although he previously had distinguished himself as a leader of the Benedictine order.

The Baum appointment to the Vatican's Sacred Congregation for Catholic Education bad been anticipated for so long that speculation on his successor has been well refined.

Front-runners include Archbishop Joseph Bernardin of Cincinnati, Archbishop John R. Roach of St. Paul-Minneapolis, Archbishop Edward A. McCarthy of Miami and Bishop James Rausch of Phoenix.

Bernardin, 52, unquestionably is destined for greater things in the church. Four years as general secretary of the bishops' conference and a term as president of the conference has left him well connected with both Rome and Washington.

An irenic personality and a remarkable ability to reconcile radically differing viewpoints have endeared him to fellow bishops as well as his parishioners.

Some argue that Bernardin and his healing touch have been reserved for the Archdiscese of Chicago, which is badly fractured under its present leader, Cardinal John Cody.

Roach, 58, has functioned well both in the St. Paul-Minneapolis archdiocese and within the bishops' conference, where he is vice president and widely expected to assume the presidency after the elections at the end of this year.

McCarthy, 61, racked up a good record as the first bishop of Phoenix when Catholics were discovering the Sunbelt, and has done well in his 3 1/2 years in Miami. By moving him to Washington, the church would open up the Miami post for an Hispanic at a time when Hispanics nationwide are clamoring for more posts in the hierarchy.

Rausch, 51, knows and loves the Washington political scene from his five years here as general secretary of the bishops' conference. During that time he made many friends but also reportedly, some enemies, who might resist his promotion. As in the case of McCarthy in Miami, Rausch's Phoenix diocese has many Hispanics aspiring to leadership.