To begin with things very clear, radars are not only what the main people think they are. Supposedly, just a way to detect enemy aircrafts. That's not a bad understanding, but it needs to be complemented saying that if you detect an enemy aircraft with your radar, the enemy aircraft will automatically detect you.
A radar is just some waves sent in the air. This waves get reflected on an object like a plane, and come back to your plane where they are detected by sensors and analyzed to determine position, speed, direction of flight, and even kind of aircraft. As an aircraft needs to have sensors to detect its own reflected waves, it also will detect any ways that are sent to it. This is the reason why when sending waves to detect an aircraft will automatically reveal our position.
This has even another problem. A radar has a certain range of detection. This is the distance in which the waves can travel in one way, get reflected, and come back with the strength enough as to provide a signal in the pilot's screen. In this way, we can say that the aircraft that a radar can effectively detect can be placed up to 100 miles, to set an example. But the problem is that all other aircraft placed between 100 miles and 200 miles will be alerted of our presence, but we will never know about their presence.
All this reasoning brings to a conclusion. There is a need to take advantage of this situation, and this is how the active and passive radar were created. An active radar is the one that actively send waves in order to detect anything place within its effective range. A passive radar is a listening one. It simply waits to receive waves from all the airplanes around that are using their active radars. This combined with a strong stealth condition can guide an aircraft to his enemy without even being detected.
Unfortunately, not in all combat situation this is a possibility. Normally the strategy involves to use the passive radar to approach targets, but when it is time to engage and fire, the active radar sometimes must be switched on in order to allow the missile to get the information and follow it. Some missiles need the guidance of the airplane's radar until they hit the target, which compromises heavily the aircraft's position. Recently, many missiles have been developed in which you simply can fire and forget. Switch for a few seconds to active radar, pass the information to the missile, fire and switch off the active radar.
Combining this methodology with a change of direction, speed and altitude just after the launch of the missile gives always the less compromise to the position of the plane. In any case, compromising the position of the plane for a few seconds is always necessary when firing, as it involves a extreme heat that infrared detectors can locate, and with health fighters like the F-22, it involves the opening of doors that get the Radar Cross Section extremely enlarged.