Freezing motion generally requires one, maybe two things: fast shutter speed, and flash at the right time. If the shutter is open for a "lengthy" period of time, anything that is in motion will blur. The word lengthy there has to be put in context, as a ping pong ball in motion can move fast enough that a shutter speed as high as 1/100th of a second might not be enough to stop its motion. To freeze motion, I would start with a shutter speed of 1/125th of a second at a minimum. The faster the object or objects are moving, the higher a shutter speed you will need to actually freeze them in a frame. It is not unheard of to use shutter speeds up to 1/1000th of a second to freeze simple motion like a ping pong ball. If you want to freeze extremely fast things, a shutter speed of 1/8000th, or possibly even higher (if your camera supports it) may be necessary.
In addition to high shutter speed, you might also want to use flash to freeze motion. If you use a flash at the right power, with a shutter speed of 1/200th of a second, freezing a ping pong ball in motion should be a synch. The pulse of a camera flash is very quick, on average about 1/1000th of a second long. The illumination from that pulse is bright enough to freeze an object at that moment, and overpower any other residual exposure that may occur as the object continues to move over the longer 1/200th second duration the shutter is open. (Note, most cameras have a flash sync shutter speed of 1/200th or 1/250th, possibly 1/500th for more advanced/newer cameras, which is the minimum amount of time required to successfully synchronize the shutter actuation with a flash pulse.)
Using flash, you can also introduce some intriguing effects into your action shots. While synced flash photos are usually limited on the upper end to a shutter speed of about 1/250th of a second, you do have the option of using a longer exposure. Try shooting your ping pong scene with a shutter speed of 1/8th of a second, and configure your flash pulse to activate on "second curtain". The resulting effect will show motion blur of the objects through the duration of the exposure, and the flash will "freeze" any motion just before the exposure ends, making the objects appear clearly at the end of their motion blur.
Regarding correcting motion blur with post processing, it is generally not possible with most common tools. Blur caused by object motion is a physical thing, not a digital or optical aberration. It is also highly random (across an arbitrary number of photos) compared to digital or optical aberrations that can be corrected with software. As such, it is very difficult to correct with software without extensive knowledge about exactly what motion was captured (i.e. object motion vectors, which objects were in motion and which were not, etc.) Given the proper information, correcting object motion blur with software might be possible, however generally impractical for real-world photography.