What is the best way to take night ACTION shots with the EOS Rebel T3?

[Kddreyfus]

Whenever I search for anything to help me with night shots with the t3i, people only ever talk about night portraits which I am not interested in.

[cicopo]

It's not the right tool for the job. Low light action is a very tough assignment, and depending on the type of action it can be very expensive to be consistently successful at capturing it. Without knowing specifics the common recommondations are to get a camera that does high ISO well & has a good AF system for low light & to buy fast lenses, as in very wide apertures (f2.8 or faster). Those lenses get expensive if you need long ones. 

[hsbn]

This is one of those situation where "gear does matter". For action shots, you'll need high shutter speed. In order to do that, you must have enough light, or faster lens and/or using high ISO. Assuming you don't want to buy new equipment, then using the widest aperture of your lens, and increase the ISO until you get the shutter speed that you want. You can use Flash to add some light.