How to connect the oscilloscope to a circuit
The circuit as drawn has no earth connection so it is isolated from earth. You can, therefore, connect any single point of it to ground without a problem.

Note that the circuit correctly shows both alligator clips connected to the same point in the circuit. If the probe and clip on R2 were swapped then R2 would be shorted out by the earths through the oscilloscope. That could be very bad in a high-powered circuit!

Note also that the probes are measuring voltages away from the common point so the waveforms will be inverted relative to each other. Most 'scopes have an "invert" function on one or both traces to cope with this situation.