How to measure current practically in a circuit
You don't need to open up the circuit at all, if you know you can trust the resistors.

If you measure the voltage across R3 you get a reading proportional to the current by I3 = V3 / R3. Or, put simply, with R3 being 1kOhm, you get 1V for each 1mA through R3.

If you measure across R2 you get a voltage proportional to the current I2, by: I2 = V2 / R2. Or, again simply, with R2 being 2kOhm, you get 2V for each 1mA through R2.

If you measure across R1 you get the current through R1. Verify that the current Through R1 is the current through V1, which is also the current coming out of V1, which is in fact I1.