How to measure the capabilities of a wall adapter?
The basic answer is "try different loads to see what works and what doesn't".  All other answers are a variation on this.

Of course you can swap out different values of load resistors, measure what the voltage/current is with different resistors.  Then graph the results.  That's the "poor man's" way to do it, and it works surprisingly well.

On the other end of the "sophistication scale", there are electronic loads.  This is a box that looks a lot like a nice benchtop power supply, but provides a load.  You can configure this load in a variety of ways (Constant current, constant voltage, resistive, pulsing, etc.).   You change the load electronically and graph the result.

A third way is to make your own electronic load box.  Again, there are many ways to do this.  Simple relays that switch in/out load resistors works.  Or you can do the equivalent of a high-wattage current mirror (or amplifying current mirror).  An opamp plus MOSFET or Bipolar transistor can be turned into a regulated load.  

All three of these options are valid.  But I can tell you this:  most people use the first approach, just sticking on some load resistors.  If people get fancy then they add some switches and a heat-sink to the resistors.  Cheap, simple, and adaptable.  

One thing to keep in mind with any of this:  It is likely (70% ?)that some sort of Polyfuse is being used to limit the current.  This is basically a resistor that dramatically increases it's resistance when it gets hot.  Run a lot of current through the device and it heats up, thus increasing the resistance.  When the temperature goes down, the resistance goes back down.  These are used as self-resetting fuses.  The problem with these is that they are not terribly accurate, and their operation depends on the ambient temperature.  So on a hot day they might kick in at a lower current than on a cold day.  Keep that in mind when figuring out how much current your wall adapter can support.