With using standard way, ie. 3rd person + gunner optic, without AA UI, nothing changed when compared to, say, Gepard and so on. You just press the assigned keybind and if the target is within tracking radar/IRST accquisition box, it will lock and maintain that lock as long as you dont manually disable it/LoS is broken.
Now as for actually hitting the target, you need to kinda lead the missile - further the target is, further you need to lead at the launch and then gradually lead less and less as the missile closes the distance.
This is due to fact that missile will burn most of its energy on climbing and once sustainer is out, you are running on what energy you managed to save. Not so much of an issue if the target is flying in a straight line but if he manuevers, missile might not have enough energy to actually hit.
If you simply leave the missile to automatically follow the center of the lock box, it will run out of energy sooner.
will just repost my mad photoshop skills to explain further.

Missile, if left to automatically follow the centre of the lock box, will fly on the blue path which isnt optimal and will likely end up with a miss if the attacked plane is fast enough. If you manually lead, missile will follow the pink path, saving valuable energy.
But standard way is double edged sword - it helps you lead the missile but its much more prone to user error as any sudden and large reticle movement will likely lead to the missile overcorrecting itself, further wasting valuable energy. But sometimes the ability to whip the missile around is desirable if the enemy is taking evasive action so…
As for AA UI guidance, not home rn so i cant double check, but you simply doubleclick desired target from the target list on the right side of the screen - if said target is viable, ie. tracking radar/IRST has clear LoS between you and target, it will lock itself onto it.
AA UI has the advantage of not having to manually search for the target alt and bearing with use of gunner optic, as the AA UI will point the camera (on vehicles that have it) perfectly at the enemy plane.
Then you just need to click assigned fire button (i think its right click by default when using AA UI, but again im not currently at home so I cant check) and the missile will fire.
There is however massive difference in guidance quality. It might be just my confirmation bias, but the missile launched and left for automatic guiding through AA UI will act like plane SARH missiles, ie. automatically leading on the target. The automatic AA UI guidance will also make smooth minot corrections, so the missile isnt wasting any unnecesary energy during its flight.