A priest somehow gets on the Bishop’s radar in the same way that a normal employee gets on a manager’s radar for promotion. The priest stands out in some way - he does a great job at some visible task, he’s excellent at raising funds, or is well connected, or presents himself especially well, shows an interest in handling more responsibility, makes his superiors look good, and/or perhaps is a member of a particular group whom the Bishop thinks should be more represented at higher levels (such as a minority, or bilingual, or traditionalist, etc.)
The priest likely gets some kind of diocesan job or task that makes him more visible to the bishop and auxiliary bishops and diocesan staff. He gets to know people.
Pretty soon when they need an auxiliary bishop or a permanent member of diocesan staff, he might get the job.
And then when it’s time to appoint a new bishop somewhere, he might get tapped for that job.
And so on… Networking seems to be a lot of it to be honest.
it also definitely seems like particular parishes might be “feeders” for diocesan jobs. The parishes in question that I’ve seen doing this are very large and have a lot going on, and usually the pastor is supervising a number of priests and deacons and a significant number of staff and lay volunteers. It’s like managerial preparation. The priest from some sleepy parish out in the hinterlands is unlikely to get called up for a diocesan job and often they will assign priests there who are either just starting out (if the priest does well, he gets a busier assignment) or perhaps are retirement age and need a less busy environment.