How can I determine if my oscilloscope is operating correctly?
Well, the oscilloscope should have its own internal function generator for calibration purposes. Usually there will be two exposed pins on the front panel where the probe should be connected. It should be explained in the manual what type of waveform you should expect. This is also important for probe calibration too. 

I don't know of any other easy way to calibrate it.

You could always mess with microcontrollers and try to generate some sort of calibration signal, but unless you have another oscilloscope to confirm that the device is producing correct signal, you can't be sure if the oscilloscope or the home made function generator or both are broken.

Another option would be to get it professionally calibrated, but that could be expensive.