Well the suitable way would be to have the PSU connected to the old DVD player innards so that its normal operational load could be running. You would then simply insert a current meter (DMM in current measure mode) in series with one output at a time and monitor the current consumption into the normal load. This will give a good picture of that that power supply was nomimally expected to deliver.
If the "old DVD player" is junked out and not available to be used for a nominal load then you have a harder job on your hands. One method to determine capability of the supply would be to put the thing on the test bench and connect resistor loads to the outputs. You want to utilize high wattage resistors for this so that they do not get hot and cause a change in the reistance of these load resistors. For this type of test you will need to simultaneously load all the outputs that you would like to use on the PSU. The idea is to start with relatively light loads and then interatively increase the loads to more and more current while monitoring the output voltage across each resistor and periodicaly checking the temperature of critical components on the PSU board. As you get to heavier loads it also pays to check each output with an oscilloscope to check each output for amount of noise and ripple.
When you reach load sizes that start to cause the PSU to get hotter than a nominal working value, increased ripple beyond more than 1 or 2% of the voltage levels of the output, or the nominal output voltage sags more than 4 to 5% then you know you are reaching the design limits of the power supply. From this check the current flow into each load resistor and you will have a close idea of the supply capacity.
For sustained usage of the supply it is recommemded to back off on the limits determined above. Also make sure to use the PSU in no worse enclosue space than it was in when in the DVD player. For exwmple if the original application had a fan blowing air over the PSU then make sure to provide as good or better environment in the re-use application.