If you're doing this professionally (which it doesn't sound like you are) - then use a power analyser (Yokogawa, Newtons4th, ZES Zimmer, Norma, etc..) - expensive pieces of kit, but pretty good.
For hobby, then probably I would build a resistive current shunt, (differential probe) and use a scope (isolation...?). Download the waveform from the scope and work out the area 'under the graph'.
If you need precision, can't afford a power analyser then probably look at the MCP3903 (we used this in a clients project, when we needed to build a basic power analyser into their product).