The web sites listed by Uncle Bob are a good source of numbers and info if you have an idea what they are talking about, but some of the concepts are not real well explained. I have worked with these for 20 years, so I will try to simplify for you.
Basic principles of to-target navigation for Air to Air intercept missiles was the question. I will start with basic missile principles.
All missiles are composed of basic parts:
Seeker, the part that looks for the target.
Guidance computer, the part that controls the missile to the target.
Target detector, the part that tells the warhead to detonate.
Warhead, the part that goes boom!!!
Safety devices, They keep the missile motor and warhead from firing at inappropriate times.
Motor, the part that pushes the missile.
Fins, the part that acts on the air to change direction. They are also called wings, fins, canards or stabilizers.
Different missile types have different names or bits and pieces added, but the above list is the basics.
The seeker can be looking for radar or IR reflections. Radar guidance signals are transmtted from ground, ship or any aircraft in the general direction of the target on a coded frequency the missile seeker is programed to look for. IR guidance seekers are looking for hot jet exhaust in low tech systems or difference from background temperature in higher tech systems. Either one will send a signal to the guidance computer of where the target is in relation to the centerline of the missile. low tech sistems will just look for what quadrant the target is in, higher tech systems tell more exactly what direction the target is.
The guidance computer takes the data from the seeker and computes how to guide the missile to the target. It will steer on an intercept course leading the target to impact the target.
The target detectors simple task is to detonate the warhead when the missile is close enough to kill the target. Most missiles have an impact detector in case of a direct hit or a radar based proximity detector for a near miss.
The warhead is designed to focus the blast in a plane perpendicular the the missile centerline for Air to air missiles, or have a shape charge for air to ground missiles to defeat armor. As blast effects are really a poor kill device, most warheads are designed with fragmentation in mind. The frag will greatly increase the kill range from inches to yards. Blast really only works if the warhead is in physical contact with the target. The frag takes the energy of the warhead just like a bullet takes the energy from a powder charge in a rifle. The frag impact the target, causes critical damage, target nolonger is capable of flying and meets the ground at excessive speeds.
SAfety devices come in many variations. They are all meant to keep the missile safe for the people using it. They keep the rocket motor from firing until the launching pilot actually fires it. They keep the warhead from explosing until the mssile has launched, clear of the launching aircraft, and in proximity to a target. The motor safety devices usually are a circuit interupt or shorting device to stop electrical signals from igniting the motor. The warhead safety devices have several parts, electrical and mechanical. The electrical parts are similar to the motor safety devices, to keep electrical signals from firing the warhead. The mechanical devices will detect the acceleration of a launch to allow the missile to get out of close proximity of the launching aircraft.
The motor in all air to air missiles are a solid fuel rigid formed low explosive. Translation - the missile is pushed forward for a very short time by the hot gasses from the burning of the rocket motor. When they talk of dual thrust, that means that on initial launch, during the boost phase, the takes off like a bat out of hell for about a second, then cruises for a few more seconds under sustained thrust. The thrust in boost phase is 20 to 30 Gees or more, depending on exact missile. sustained phase thrust drops to 1/3 or less of boost phase. In the movies where you see the missile fall out of the sky as soon as the motor burns out is pure hollywood. At that point, the missile will coast for several minutes, until the battery is exhausted. The missile will travel many miles this way.
The control fins are used to steer the missile. The wings are stationary and the fins or canards move. They are hydraulically or pnuematically powered, depending on missile type. The fins are mounted in pivots that recieve signals from the guidance computer, telling them which direction to turn the missile.
In use, the pilot finds his opponent by radar.
He turns his aircraft to point toward the target.
He selects a missile to track the target.
The missile will lock on when the seeker has identified the target and the guidance computer calculates it can reach the target.
At that point, the pilot will hear the lockon tone that means he can fire the missile and expect to kill the target.
He will trigger the missile.
The safety device will send a signal to the rocket motor causing an igniter to flash through the motor firing.
The missile battery will activate, powering the missile electronics.
When the motor generates enough thrust, it will break a holding pin, allowing it to leave the launching rail.
Teh umbilital cable conneting the missile electronics to the aircraft will break.
The warhead safety device will depress from the G forces, allowing a timer to run arming the warhead when the missile is clear of the launching aircraft.
The seeker will tell the gudance computer where the target is.
The guidance computer signals the fins what direction to ster the missile so it will intercept the target.
The target detector will look for anything large enough in close proximity, sending a signal to the warhead safety device when a target is detected.
The warhead safety device will send a signal to the warhead detonators causing the warhead to detonate.
The expanding gasses of the warhead will impart high velocity to the fragmentation warhead casing, sending them out in a pattern to hit the target.
The frag hits the target, tearing holes in many critical systems rendering the target unable to continue flying.
The target hits the ground in a way to defy all the kings men from putting it back togather again.
Missiles for use in space would have to be made differently, as the fins would have no air to bite to turn the missile.
The latest solid fuel air to air missiles are starting to use directed thrust, but that works only as long as the motor is burning, then they rely on fins for turning.
Light mass would still be very desirable. Less mass means more Gee per thrust, higher velocity, longer range so more efficient.
As most ships would have a skin resistant to micro meteors, normal frag warheads would be ineffective, so a shape charge would be needed.
The only effective near miss warhead would be a nuke.
Space to space missiles would have to change, but not as much as you might think.