If your turntable has built-in speakers, try connecting a set of speakers to the turntable, or using headphones (if your turntable has a headphone jack) to see if the sound still only comes out one side. If you get sound from both sides with the external speakers, or the headphones, this means one of the built-in speakers may be blown.
If you still only get sound from one side, check the stylus. If the needle is bent, or leaning to one side, it will not pick up the left and right audio channels evenly. Replace the stylus with a new one and you should hear both sides.