you haven't shown what the load is on the high voltage side. to measure current your shunt resistor will be connected between the low side of the load and ground. you haven't said what the "high voltage" is, so be aware that most multimeters can be damaged by voltages above 400V. the meter will have that information printed on it near whewre the probes connect, and may say the max voltage is 400V (usually 400V for a cheap meter, but may be as high as 2000V for a really good one). you don't want to exceed the max voltage printed on the meter. you will need a "True RMS" meter to measure the output accurately, and the measurement bandwidth of the meter needs to be >20khz. most cheap meters only measure average voltage, and "fudge factor" it for the readout, and most meters only have a measurement bandwidth between 500hz-1khz.
oscilloscopes also have a maximum voltage that can be measured, usually around 1000V, and that should be marked somewhere near the input connector.