The following options seem to be the most common approaches to hiring a head football coach (NFL or college):
Option 1: Make a list of head coaches recently fired in the off-season. Analyze the performance of each and pick the coach you can make the most excuses for not winning at his last stop.
Option 2: Pick from the list of network analysts that have chosen to hang up the whistle. Why wouldnt they want to come back to coaching where they will make the same money but have to work five times the hours with 100 times the stress?
Option 3: List the best offensive and defensive coordinators. Analyze each coachs strengths versus your teams current weaknesses. Whichever coach fills the gap the best, hire him. Great coordinators have to make great head coaches right?
Option 4: Analyze current head coaches doing the most with less that would be willing to make a move for a bump in money and hopefully a better chance of winning on a higher level. For NFL GMs, this could be similar to going after the most accomplished college coaches.
Option 5: Promote from within.
So what is the best method, or are there methods that could be more successful that arent being tried? I personally feel that the coach hiring process is usually rushed, and not looked at as hiring a CEO of game day operations. The X and O talents of a head coach do not necessarily have to be elite as long as the overall vision matches that of elite coordinators. There are obviously exceptions where the head coach is the General of either Offense or Defense, but is that the best scenario? If a coach is so wrapped up in calling plays, is he fully focused on the entire team? Should new blood be considered more often in lieu of recycling the same guys over and over?
So, you are named the A.D. or G.M. today and your team has a coaching vacancy, what would be your plan to hiring the next great coach? feel free to focus on College, Pro, or both.

Comments
Is Bud Foster's approach of "sign that guy we found in the aisle at Walmart" an option? I'm pretty sure that's what the Raiders and Jets have been doing for for almost a decade now.
Option Nuclear: Hire Bud Foster
All of the above? Make a list of the top 50-75 best candidates (including current FBS coaches, FCS coaches, NFL coaches, FBS coordinators, NFL coordinators, other people currently in your department, etc.). Cross of the ones you know won't happen (ie, Saban or Meyer). Reach out to sources to gauge interest. Conduct Interviews. Progressively narrow the field. Make a selection.
Option 6:
Has technology reached this point yet?

Hire a HS coach from Texas
Whatever Whit thinks is what I'm good with
We're hiring a new coach?