This is quite easy to do. I prefer firing coaches at the end of the year, but you can do it whenever you feel like during the season. You CANNOT do this during the off-season, so I tend to do this immediately after the national championship game, and prior to going into off-season.
The general idea here is that the game has a feature to create new coaches and assign them to a team. If you decide to leave that team, the game will have to hire a new coach from one of the FCS teams or other coaches available in the "COCH" database that is not already assigned a team. This allows you to replace teams that are failing, with a new coach and their own set of coaching playbook strategies and recruiting/training attributes and hopefully rebuild the team up.
So first off, you just need to find out which teams you want to have their head coaches fired at. Write them down.
Next, go to Coach Options in the Dynasty Menu, and select Positions. Then press CIRCLE and Create a Coach. Just press Start. You don't need to do anything more here, since you'll delete this coach anyway later.
After you're done with this, select the coach, and press X to find a job. You should have every school available to you. Now just pick the team you want to fire, and get hired there!
After you're done and now own that team, click X again, to QUIT the job. Then you can delete that coach.
You can also just find a new job and continue down your list. Just note that each time you do this, you can only hire onto teams with less prestige stars as the previous one unless you delete and create a new coach again.
Continue this until youre happy. Then, you can back out to Coach Strategies and cycle through with the trigger buttons to see who each team hired to replace their previous coach!