There is tons of info available at the library on how they work and how they are built so I'm going to give you is how they are tested.
I was what P&WA called an instrumentation tech. All engines military or civilian must be extensivly tested before going into service. The same holds true for a new or modified part. What the testing involves or how long it goes on depends or so many factors I'm not even going to try to explian but basically a new engine can get tested for up to 3000 hours (running) and under very strict testing parameters. A new or modified part a lot less but it can be extensive depending on the part.
1. A new or modified part.
Comes from the assembly floor to the test area (where I worked) installed in an engine. Depending on what and where it is it can have a few or a lot of sensors on it. Sensors to measure temperature, pressure, stress (strain gauge), vibration, and others I can't tell you about since they are (or were) classified (I had a secret clearence). Depending on what and where it can take a long time to assemble an engine with many parameters as the wires, tubes, ect must be routed out of the engine in such a way as not to interfere with its operation. It can be a nightmare. The engine is mounted in what is called a strongback and this is then mounted in the test stand. Engines are hung from above. The entire assy is mounted in such a way that thrust can be measured. The stand crew (operator and 2 mechanics) then connect all the various systems, pipes, cables, etc. They only exception is the ones I measured (strain gauges and vibrations). I ran a data recording system built into an 18-wheeler trailer that could measure over 100 parameters on a single tape deck and either 60 or 120 IPS (inches per second). Obviously this was a very expensive tape deck. Once everything is conneted, calibrated, checked out, and signed off (lotsa paperwork, lol) it was started up. Lotsa eyeball monitering at this time. Engine was left at idle, N-1 (low rotor) around 4000 RPM - N-2 (high rotor) at around 9000 RPM for 5 minutes (during which an inspector would do a walk around leak check) then shut down. Any leaks (rare) were corrected and the oil level check. If all was well they ran the test program taking data points such as a static (compter system reads all parameters) or a dynamic (computer reads selected parameters while the engine makes either a slow accel or decel or a snap accel or decel. Thisd continus until the program is complete where the engine is dismounted, transported back to the assy floor, and dissassembled to check the part.
2. A completely new engine. Can takre up to a year to assemble. The first 1129 (a derivative of the F-100) had over 3000 parameters on it. So many that they had to use all the computer lines from both sides of the test stand (2 engines per stand). When done you literally could not see the engine from the side for all the cables. A static normally takes 10 to 20 seconds. It took 5 minutes for this one. They wouldn't go above idle for almost 2 weeks then finally started creeping up (ands mean creeping). Why? Darn thing cost over $50,000,000 to build, assemble and mount in the test stand and that $$$ was on P&WA. Once it gets to idle its USAF $$$.
3. I worked on the J-52, J-58 (in the SR-71 Blackbird), F-100 (in the F-15, and F-16) TF-30 (in the F-14) and the new engine in the F-22 Raptor (super neat engine and plane). It didn't have an afterburner and again it stayed at idle for quite a while before accelerating. When the final testing was done they cranked it up to full military power and just let it roar to see how long it would take go go kaboom (bout 18 minutes if I remember correctly).
4. Jets are very quiet at idle. You could go on the test stand (with the operators permission) of an F-100 at idle without any ear protection at all. All you would hear is a low pitched hum - a high pitched screech would come out of the front and whatever you do don't look up the tail, lol. An engine at power is loud loud loud. We had mufflers in back ($1,000,000 each). I lived over 25 miles away and could sometimes hear them testing. The high frequencies get absorbed by the flora and fauna but the low frequencies bounce between the ground and cloud cover (like a wave guide) and can travel quite a distance. More when it raining (heavier clouds).
5. How do you attach a sensor to a rotating part. Extension cords don't work, lol. Two choices:
A. Telemetry (not the most reliable thing it the world tho it can work). Probablms are: it uses FM frequencies which can get interfered with by local radio stations, the transmitters aren't tiny so location is almost always a problem, and they tend to have a high level of noise along with the signal (which is usually in the millivolt range).
B. A slip ring. This is mounted on the front of the engine and has a series of metal rings that rotate with things that brush up against them (which do not rotate). Works quite well. Not nearly as noisy and you can have up to 100 channels. Takes a while to install tho.
6. Bird ingestion tests. A calibrated starling (soft lead BB's are inserted into the dead bird to get the weight up to a standard value) and shot into the engine by an air cannon. The engine has to be at full military power (after burner off) and after the bird hit it must return to full military power or it fails. Quite impressive to watch tho the assembly floor guys hated tearing one back down as they stunk to high heaven.
7. Do they blow up? Yup. Sometimes impressivly depending on what fails (usually a rotor). I've seen rotor blades sticking out of an H-beam like knives in a tree. If it cuts thre fuel line the entire test stand can be enveloped in flames. A test stand is strictly off limits at anything other then Idle. Stands all had a large fire system (water) except the stand that tested the J-58 which had dual Halon systems. However - titanium metal burns and can't be easily put out with water so they had covers for the front and rear then few CO2 into the engines to smother the fire.
Nuff for now - let me know if this is what you had in mind.
Ben