Initial experiments with an oscilloscope
The first thing I would do is read some literature on how scopes work.  Tektronix has a good white paper called XYZs of Oscilloscopes.

Next, you should hook up a function generator and figure out how the different display controls work.  This includes the Y scale [Volts] and the X scale [Time].  

Once you feel comfortable with those get comfortable using the triggers.  Triggers allow you to capture a waveform at a certain point based on your trigger settings.  As an example, you may set the trigger to start capturing a waveform once it sees a rising edge at 300mV.  If you are on single capture in "normal" (not auto) mode it will freeze that waveform on the screen until you push a button to capture another one!  Being able to use triggers is something many new engineers don't master, effectively making scopes useless to them.  Get good at them and you will be teaching the rest of the class!