How to measure max current of a power supply
The correct way is to analyze the schematics of the power supply, noting the max current/voltage/power that each device is being subjected to.  Make sure you look at these numbers over the entire operating range (Vin, Vout, Iout, Temperature, Humidity, airflow, etc) as well as over the tolerances of the components that are used.  

Once all of the component maximums (and your operating margin) have been figured out, you know the absolute maximum rating of the device.  But that is not the end.  You next figure out how to properly "derate" components.  For example, it is common to derate a resistor by 50%.  Meaning that if a resistor is rated for 1 watt, you will only allow 0.5 watts.  Same goes for caps, transistors, MOSFETs, etc.  Also, some components like electrolytic caps will have a significantly increased lifespan if derated (Voltage, current, and temp!).  

At this point you can calculate the actual maximum power rating for the supply.

What you absolutely do not want to do is to put the supply under a high load and see if it "can handle it".  Even if it does handle it for that moment, it might be permanently damaged-- and damaged in a way that will only show up later when you are away and your house burns down.  

If I received a power supply that wasn't marked, I would never power it up.  Instead I would throw it away.  Electrical Engineering has some hazards that are not worth tempting.  This is one of them.