The Following Summary of the F-117A Nighthawk is taken from www.af.mil

The F-117A Nighthawk is the world's first operational aircraft designed to exploit low-observable stealth technology.
The unique design of the single-seat F-117A provides exceptional combat capabilities. About the size of an F-15 Eagle, the twin-engine aircraft is powered by two General Electric F404 turbofan engines and has quadruple redundant fly-by-wire flight controls. Air refuelable, it supports worldwide commitments and adds to the deterrent strength of the U.S. military forces.
The F-117A can employ a variety of weapons and is equipped with sophisticated navigation and attack systems integrated into a state-of-the-art digital avionics suite that increases mission effectiveness and reduces pilot workload. Detailed planning for missions into highly defended target areas is accomplished by an automated mission planning system developed, specifically, to take advantage of the unique capabilities of the F-117A.
Some pictures released by the Serbs of the F-117.
That's a summary - now lets deal with some of the Myths
Q.1 Stealth Fighters are invisible on Radar
A.1 Well the news is that they are NOT invisible on radar
The stealth features on the Nighthawk work in two ways, the first is to try and not
reflect any radar energy back to the transmitter. If it cannot do this with the radar
signal then it tries to reduce the amount being returned by absorbing as much as as it
can. You can see the effect of the first of these techniques in the visible appearance of
the Nighthawk. The sharp angles and triangular shapes that compose the structure of the
plane as designer to reflect the radar pulses away. The second techniques is not so
visible and that is the actual structure of the plane is made out of Radar Absorbent
Material (RAM). This absorbs radar energy and converts it to heat.
Q.2 So if its not invisible why does it not get shot down
A.2 Because even through it is not invisible on radar it is very hard to see with certain radar systems.
Radar systems can be divided into two basic types: - Surveillance and Tracking radar's. Surveillance radar work at longer frequencies such as D/E Band ( L Band) while Tracking radar's work at much shorter frequencies such as I/J Band ( X-Band).
The function of surveillance radar's are to give the operators a overall view of the the area that they are looking after. These radar's indicate to the operators where they should point the Tracking radar's. Is is the work of the tracking radar's to guide the missiles to the target.
The Nighthawk is visible to Surveillance radar's however it is a very bad target for tracking radar's. So though the operators can tell that there are stealth aircraft around they cannot get their tracking radar's to lock on long enough to guide a missile into it.
Q.3 So what happened to the Nighthawk over Serbia?
A.3 It seems that the US had broken one of the golden rules of operations NEVER FLY YOUR STRIKE PACKAGES OVER THE SAME ROUTE DAY AFTER DAY!. They seem to have been doing this. The Yugoslavs moved a SA-3 battery into an ideal location for this and used a combination of radar and optical guidance to launch 4 SA-3 missiles at the Nighthawk. The optical system on the SA-3 is rated at 25Km under ideal situations. One of them exploded near the Nighthawk, the pilot reported that this damaged the control systems making the plane unflyable. So there you go - a 1960's system shot it down using a combination of common sense, operator skill and luck.
A.4 Then why has the US military not said this
Q.4 Well some parts of the US Military have been building the stealth planes up as being invincible. Its a bit embarrassing to have one burning in a Serbian field!
Q.5 Do the Russians have some radar's to track Nighthawks?
A.5 The Russians have
a couple of systems capable of detecting the F-117A bomber. For example, there is the
mobile 1R13 EWR station (capable of providing targeting info to SAM systems and Air
Defence commands). This station can also easily guide an interceptor to the F-117A.
Q.6 But they say the F-117 has a cross section of a ball bearing!
A.6 How often do you see a ballbearing doing Mach 0.8 and dropping bombs? The F-117A isn't quite invisible to radar - it has a reflection, but that is usually classified as static (a reflection similar to that of a flock of birds). Of course, if the plane gets too close to any radar (or goes straight at it) it will be detected by it, although at a short range.