Looking at airshows, particularly red arrows, they manage to fly side-by-side in perfect order and speed, turn at exactly the right time, and generally be perfectly synchronised, how?

practice practice practice

l was stationed at pensacola naval air station. that is home to the blue angels computers and good people on the ground and well trained pilots

Lots and lots of lovely practice.

Most of the flying is made possible by the onboard computers in the planes. Without them nearly any type of flying would be nearly impossible. The Blue Angles are some of the most trained pilots in the world and know exactly how to menuver their planes. The pilots do the flying, the computers make sure all the planes stay at a constant and smooth velosity and altitude and the ground crews coodinate the stunts and menuveurs.

As u get close to the other aircraft. You attempt to identify two locations on the other aircraft. Perhaps the outside edge of his flap seal & then the corner of the cockpit window. This creates an angle between ur eyes & the other craft. You then attempt to maintain this angle by using ur controls & throttle.

You no longer reference ur instruments or navigation. It is done by the lead aircraft. Your concentration is on this angle u created. Radio cues r given as to when to begin turns etc. With practice it can be done well (ie blue angels).

Training, Training, Training.
Demonstration teams, such as The Thunderbirds, Blue Angels, Red Arrows, etc. r made up of highly experienced pilots.
Modern aircraft have lots on nice electronics to make them the weapons systems that they are.
But when in comes to precision flying in formation, It is all VFR with their head up, using the aircraft in front of them as point of reference.
The Leader makes the calls for turns & maneuvers. Lots of the time its follow the leader.

Gary & Dennis r spot on. It is done by7 reference to lead, & as others have said by much practice. ''Computers'' make it easier to execute more refined control surface movements, but it is still stick & rudder work. AFA most demonstration teams r concerned, just about any Mission Ready/Instructor Pilot in a fast-mover could do the routines. But what the services want is a poster-child (in a good way); that can represent the best of that service -goes for maintainers/loggies as well.

How do the military fly in such precision. It is called training as a team. Each man know what the others will do. And there is only one leader. The Blue Angles and the T'Brids have hunders of hours of fliyng in the planes they fly.
Start with to plane. They fly the slots. Then another plane is added, ect. They learn each stund this way. The boss is the number one plane. He is the one that calls the signs when to perpare and excute.

they start by getting lots of flight experience, then they walk through their flight on the ground so that each pilot knows what is expected of them, & what to expect from the others, & then they practice, practice, practice. once they finish practice, they go through an evaluation of their flight routine, & then they practice more. then they evaluate their flight routine again, refine it, & practice more. eventually they get to the point where every maneuver becomes second nature & they know instinctively what each member of the team is doing, & how to prevent mistakes. they also learn to fully trust their team mates, & the team leader.

You blindly follow the leader. Normally, close formation is flown at a distance of six feet along a determined angle from the leader. The leader always briefs his formation in great detail regarding the mission routing, heights speeds etc. Once in the air all turns & maneuvers r called out prior to execution. Speed changes r also called out over the radio. The following aircraft maintain their stations using power & the controls to stay at their pre-determined places.

Finally, a lot of practice goes into formation flying & a team spirit is developed between the leader & his formation. The leader has to be an excellent pilot & command the trust & respect of the members of his formation.