I have a point and shoot and need to know what are the best settings to shoot circus acts. I tried to shoot everything in AUTO or SCN mode on the OLYMPUS SPZ 800, but the results are not clean.
Here is my shot.
You are trying to shoot a difficult situation with a very limited camera which you cannot control, so there really not much you can except get a better camera. For one off events, you can even rent a DSLR and lens but you off-course would have to know how to use one!
Your example, the camera chose a high shutter-speed to freeze the motion of the performers. That is reasonable option but to do that it had to raise the ISO to 800 which is why the image is so noisy and low contrast.
Had the camera chosen a lower ISO, the image would be clearer but the performers may have been blurry because of their motion. There was probably a slightly better setting it could have chosen but you have no way to enforce that.
The bottom line is that moving subjects in low-light is the most stressful for cameras and even high-end DSLRs can struggle.
The main problem for shooting a scene like that, is that the main attraction is lit, and most of the surrounding is very dark. Generally this will fool the camera into trying to expose to include something from the surroundings also.
The auto mode will frequently fail you, to get a consistent result you would need a manual mode. Note also that although the circus artists seem to be very well lit, that's because the surroundings are so dark. The light levels are still way below daylight level.
You could also try something like a portrait mode, which should try to get the closest item well expoised and mostly ignore the surroundings, but that also relies on the ability of the camera to automatically determine what's actually important in the image.
just follow these simple steps on your camera if it supports
1) get the auto-ISO turned off and make sure you set it to the highest
2) in the scene selector - select "sports mode" or "night portrait mode"
3) keep your camera as steady as possible and make sure you are as close to the subject as possible
4) also make sure you do not zoom much.
these conditions and settings tend to change as per the ambiance , so consider this an experiment and try it out. photography is all about experiment and learning :)