I'm not sure how helpful this will be, as I'm not sure I really have a step-by-step process and I'm not very good, but here's what I usually try to do.
First, don't let him get behind you at the start, that makes it more difficult. Second, get really comfortable with lag pursuit, and don't feel like you have to keep him in your gun sights the whole time. That usually keeps me from turning too much and getting too slow. For example, if he's diving, then pulls up, I keep diving until I'm about where he pulled up, to maintain energy levels. I'm not a pro by any means, but I have been successful on that TE. Then again, it could just be weak AI.
Here's a video of the last part of one of my TEs that was successful, in case the views give you any ideas. You can see I made plenty of mistakes, but still managed to keep him from shooting me down.
No single drop of rain feels it is responsible for the flood.
In sustained turning rate the F-16 has a tiny but real advantage. You are almost peers. Corner of 440 KT is max instantaneous rate. It's a nice luxury but you cannot maintain it in a dogfight, don't even try. To sustain corner you'll have to fly very bad rate and a large radius. Your potential to turn at any moment will be wonderful but potential is of little help when on fire and full of holes.
Due to the very good low speed handling of the MiG (similar to F/A-18) it's recommended to attempt an energy strategy, patiently gaining angles at max sustained turn or nearly so. Bleed from pulling excess angles affects all fighters but the Fulcrum suffers from this more than the Viper. Pull lead if airspeed if high or aspect is low, bid for lag if airspeed drops or heading crossing angle grows. Use the vertical when an energy advantage develops. Keep is near 350 if you can. Don't get slower than 250 if you can help it.
Use the vertical when an energy advantage develops
can you explain in more details by energy advantage? is it when the enemy is in lower altitude than mine?
Energy is the sum of your speed and height. An energy advantage means that the sum of your speed and height is better than the sum of his speed and height. That means estimating speed and height of both you and him and knowing the conversion factor. It's more of a gut feeling that comes with experience. Usually as you and the MiG go round and round there will be some vertical wobble to the fight, pointing nose low when you need the turning rate due to gravity and nose high to convert some speed into height and reduce your radius. Over time an energy advantage means you'll be able to stay higher than your opponent and he will be unable to point up at you. Given enough energy you have the "over the top" potential where you can do loop like maneuvers and maybe he can't. Then it's like a fist fight with long arms, you can do things he can't.
It's called a knife fight in a phone booth for a reason. Dogfighting is like bad sex, quick, violent, and exhausting. Punch off all external stores (fuel/bombs), MAXAB and leave it there for the most part. Fly like you have infinite fuel meaning only throttle back if it helps you tactically. Trying to dogfight economy just means it takes twice as long and burns more gas. The fuel savings come from minimizing the time. It's not unusual for a turning fight to be the only combat you do that day, show up with 7000 lbs and leave with 2000 a couple minutes later but leave in one piece. Dogfighting is one step away from ejecting, something went wrong, forget the mission, survive.
You have two choices regarding your fuel when it comes to a dogfight -- use it (smartly!!) in afterburner or have fun watching a big fireball that used to be your F-16.
I think it's the same with countermeasures --- use it or lose it.
While the F-16 can do a high G turn, it doesn't mean you have to do it all the time. Like I said, sometimes you have to lay off the G's to stay in cornerspeed but that's where the F-16 gains the advantage.
As for ACMI files, do one yourself. Start off heading 000, 15,000 feet, 300 knots. Punch in the AB, make a level turn, but keep it at (or as close as) 300 knots. See how long it takes you to do a 360-degree turn back to heading 000. Do it again but start at and try to keep 400 knots. And again at 500 knots. And then do it again three times but this time, don't bother about keeping your speed, just yank that stick back as far as it will go. Compare the results. Share with us your findings!