It honestly will vary by state and department. In my state, the only across the board standard is the physical requirements for the academy. Every department has it’s own testing and hiring process.
Some states do a civil service exam that is good for every department in that state. Where I’m at a short process is about 4 months, with 6 being the average.
The background check is usually the longest single phase as it depends on how many investigators there are and their workload. If you apply to a state some distance away, they probably aren’t going to pay for one of their detectives to fly to your state and interview you and your neighbors.
Locally, the smaller the department, the shorter the process. Where I live the Sheriff hires who he wants and the process is really just for show.
Basically, I cannot give you a definite answer as my experiences are with my own state only. I would say that you should expect a process to take approximately six months no matter how bad a department is wanting recruits.
@JMaier31 can probably offer some more insight.