Sports is one of the more difficult areas of photography because it is very fast paced, and super demanding on gear. It would be very helpful for you to tell us what gear you are shooting with, as it will allow us to offer better advice. However, there are a few rules of thumb for sports you need to know (I will explain each one briefly):
-Fast Shutter
-Large Aperture
-High ISO (as a result of the two above...)
-Continuous Autofocus (back button if your camera allows for it)
Why?
A fast shutter (anywhere from 1/320-1/1000 in most cases) will, as you said, freeze action. For baseball 1/500 should be fine, unless you are trying to capture the pitch or the batter, in which case you'll need closer to 1/1000. A fast shutter lets in less light, so in order to compensate for this you also need a large aperture. Having the large aperture will also separate your subject from the background. Your shutter and aperture will remain fixed since it is a night game and the lighting will be constant (and mostly consistent, there may be some dark spots) which leaves your ISO as the only variable. Set your ISO to as high as possible without having too much grain or being too underexposed (too dark). You *will* underexpose slightly to allow for a faster shutter and there *will* be image noise, it's about finding a happy medium. You can compromise freezing action by going to a slower shutter (no slower than 1/250, realistically 1/320 if you want to use them seriously) to compensate for having a lens f/4 or slower, or for a lower ISO.
As for the backbutton focus I mentioned, some cameras have the option to set a button on the rear of the camera to turn on the AF, rather than your shutter button. That allows for you to control when the camera autofocuses, so if something runs in front of your subject the camera will not refocus. Check your camera manual, or let us know what you are shooting with and someone will know.
Good luck! Post pictures and let us know how it went