The first thing the priest would want to do is to get to know you a little bit, find out a little background about you. He’d want to find out why you wish to be Baptized. The Catholic church would first want you to be educated as to what Baptism is and what it is not. In order to receive a valid Sacrament within the Church you first need to understand it and be properly disposed to receive it. An example of this would be, you walk in to see the priest and ask to be Baptized. One of the questions he is going to ask you is if you have ever been baptized before. Since you can not be Baptized validly more than once, this would be vital information. Since re-baptism is a sacrilege.
Now if you were in some sort of condition where death was imminent, then yes a priest would probably error on the side of caution and do an immediate baptism providing you had not been baptized before.
Once your are properly educated, then he would most likely find you an appropriate sponsor/Godparent and schedule you for the rite of Baptism if there is an immediate necessity.
The norm would be though to go through R.C.I.A (the rite of Christian Initiation for Adults.
Hope this helps.
