This guide will not describe advanced techniques and theory, it will only tell you things that work most of the time in practice, and in practical terms. It will not describe all alternative methods and styles either, just one method that works pretty well. It also assumes you are fairly new at this. It won't make you unbeatable, but it will make you a hell of a lot better.
The setup:
First things first, you need the right hardware configuration. I will list two configurations I find ideal, but they might not be perfect for you.
Mouse and keyboard:
mouse wheel up = throttle up
mouse wheel down = throttle down
right mouse button = flare
w key = look up
e key = spoiler on when pressed
f key = flaps
everything else is up to you
Joystick+keyboard:
POV hat assigned to view
trigger assigned to fire selected
easily accessible button assigned to flaps
easily accessible button assigned to spoiler on when pressed
button assigned to flares
For your plane:
Something agile, keep the fuel long enough to get to where you're going and be light, often 50% or even less. Less fuel makes you lighter+turn tighter. Don't carry a lot of weapons because they also reduce turn performance (they add lots of weight). Don't get in a dogfight against an f-16 when you're in like a mig-25 with a fuckton of weps and fuel, you'll die in four seconds.
While in flight:
1.I strongly recommend you fly using full afterburner. This gives you more speed. You always want to be as fast as possible, because it makes you turn faster, which is better.
2.Next thing is to turn first at the merge. The merge is the first time you turn into your enemy. For example, if you and your enemy are flying straight at each other, the point where both of you pass each other is the merge. After this point you are both turning. Turn before the other guy turns, this gives you a better spot in the turn circle. And when you do turn, make it so that your wings are perpendicular to the horizon, then point your nose just a little above the horizon or a little below the horizon then pull up as hard as possible.
3. Deploy flaps after the merge turn. It makes you turn tighter (gives you more lift)
4.Never lose sight of the other guy or you will die, so use your look up button as much as needed.
5.The turn circle is a circle in the sky you are both turning along. Avoid leaving this circle as much as possible, because that is a break in your "geometry" which any opponent will exploit. In short, any time you are not turning as hard as possible into your opponent, you are running away. Running away means you just lost the fight.
6.Shoot whenever you get a chance. Sure, sometimes it's a little wasteful, but wasting a little ammo is better than being dead.
7.Imagine a vertical red line in the center of your screen. This is more or less your "lift vector" but we won't get into that. Continue to imagine that line on your screen when you look up. If you always keep your enemy on this line, you will have many chances to kill them. Here is a visual:

you don't need them on there 100% of the time, but at least about 80% of the time to close the distance. As you get better, you'll come to see that at times it is better to keep it in front of them, and at times behind them. This is alternating between the ys iterations of lag, lead and pure pursuits.
8. You turn tighter when you're going up, and you turn wider when you're going down. However, you also gain speed when you go down. Whenever you have enough speed to pull it off, you should turn up to gain the positional advantage. Whenever you need to speed up, turn down.
9. Anticipate where your enemy is going and cut their turn, while also doing all those other things.
10. If you are above your enemy and turning into them, don't be afraid to use the spoiler when pressed key you assigned to "perch" on top of them and get some shots in.
Anyways, the goal was to keep this simple, short and non technical, so that's it. Follow those 10 rules well enough and you can kill most people. Don't use them to be a dick.