How long a convert is required to wait depends on the convert in question. A Greek Orthodox priest who entered the Church is already ordained and may have to wait only a short time to be granted faculties to publicly celebrate the Catholic sacraments. An Anglican or Lutheran clergyman may have to wait much longer for a dispensation, if he is married, and for ordination. A layman without a clerical background goes through much the same process as any other Catholic layman, although recent converts may be asked to wait a couple of years to give them the chance to live the Catholic life and in order to make sure their conversions are not fleeting.
I recommend speaking with the vocations director of your diocese, or, if you are interested in becoming a religious order priest, of the order in which you are interested. The vocations director will let you know what requirements you are expected to meet.
