I started playing Inquisitor as a priest and would love to know how to get promoted and by whom for example in Act 1?

In Act I you can become Inquisitorial Prosecutor. To start off, ask Jeremiah in front of the Hillbrandt's church or Vallarian inside the church about the promotion. You will receive a quest to bring back the Monstrance of St. Orthenius that was stolen from the church and to apprehend the thief. Once you complete that quest you will also have to pass the test of canon and secular law.

*SPOILER*
To find the Monstrance of St. Orthenius, you have to kill the undead Bishop Herbertius in the tomb at the Hillbrandt's cemetery. After that talk to Romius west from the Hillbrandt's church.