You may want to start off understanding a bit more about oscilloscopes. I am not aware of any tutorials specifically for the DS0203.
http://www.instructables.com/id/Oscilloscope-How-To/ is a simple general tutorial. Although it is based on a more traditional scope than the DSO203 the controls and principles are the same.
For power supply monitoring you need to think about what aspects of quality you wish to measure or check.
There are a number of characteristics you might want to think about
a) Basic actual output voltage; how close is it to +5v
b) Static regulation under load; how does the voltage change when you draw different amounts of current from it.
c) Dynamic regulation with load changes; e.g. does the voltage dip and recover when the load current increases
d) Noise and ripple on the output voltage
a) and b) are really best measured with a multimeter. You can measure these with the DSO203 but it won’t be as accurate and you need to calibrate the DSO203 anyway.
d) Can be measured with the DSO203. You are best switching to AC coupling on the input. This removes the DC component and allows you to increase the sensitivity of the input channel so that you can see what noise and ripple is on the input. In DC mode the 5V will move the trace off the screen as soon as you go below 1v/div, but in AC mode the basic trace position doesn’t change and you can increase the sensitivity down to 50mV/div. Typically the noise from a simple switched mode power supply is around 50mV so you can then see it clearly. Changing the timebase allows you to see the characteristics of the noise. There may be hum components (100Hz) which would be seen with a timebase of 5mS/div. There may be high frequency switching noise if it is a switching power supply. Typically these are 100KHz or higher and would be seen clearly with around a 5uSec/div timebase. It can be difficult to trigger on noise signals unless there is a strong frequency component. It can be worth just setting the timebase to single-shot mode and pressing the run button to get just a snapshot of the noise to view.
c) Is also best measured with AC coupling as the voltage change under load maybe be fairly small. The best method is to be able to switch the load on and off under control so that you get a repetitive change that you can trigger on. If you were going to do lots of measurements it would be worth building a load circuit out of say a transistor and load resistor. This could be controlled from the frequency out of the DSO203 so that say it switched on and off at 1Hz rate. This would make it easier to see the effect of the load changing. If you don’t want to do this then you could set to single shot and the trigger level to manual and set it say just below the baseline trace so that it doesn’t trigger. Then connecting a load should trigger it if the voltage dips below the trigger level. I would set the timebase to something like 1mSec/div to start with and then change it so you see the whole reaction to the load change.