Measuring noise of audio preamp power supply
The simplest method is to use an oscilloscope. Basically connect the oscilloscope to the output of the supply and look at ripple and noise. You need to have the power supply under load; either full load or representative load of the pre-amp you might want to use.

I'd also consider building a battery powered signal amplifier that is quieter than your pre-amp to act as an amplifier when using the o-scope - a lot of modern cheapish digital scopes appear to have about 20mV ripple and this is too much for making measurements. The type of amplifier I'm talking about is a low noise, instrumentation amplifer working differentially and looking at the noise on the power supply output. The amp (maybe gain of 1 hundred) would output to the o-scope.

If you want to go a step further, you might want to try and inject noise onto the power supply's output - this will tell you how resiliant the power supply is to load fluctuations in normal conditions. For this I'd use a 1Vp-p squarewave or sinewave signal generator connected to the power supply output via (say) a 100 ohm resistor. Use the scope and see what sort of signal you can impose on the power supply's output. Vary frequency all the way up to about 10MHz and see if there are any weakspots where the injected signal might cause the power supply output to appear weaker. Up to 10MHz - I know you are testing a power supply used for audio but it's best to cover the full range to which the pre-amp might be expected to operate.

As this is just a power supply for a pre-amp I wouldn't expect surges of amps to be required of the power supply but if there were I might consider doing a heavier load test with a relay and power resistor. The relay would switch in and then switch out the power resistor in order to subject the power supply to a single power transient - I'd use the scope to see how well the power supply coped. I'd be interested in how much voltage it dropped when subject to the heavy load and how much it "recoiled" when the load was removed. Also, when the load was removed I'd look for for ringing because this might indicate a power supply that is potentially unstable.

How well can the power supply cope with AC supply voltage and impedance variations? This is a whole new ball-park and to add to this; how will the power supply cope with transients on the power line, ESD, milli-second power drop-outs, RF interference etc.. To do some of these tests properly you would to create disturbances on the AC line and this can be done in a home spun fashion but for susceptibility to RF interference you'd ideally need an EMC lab. You can hire an ESD gun quite cheaply (or make your own with a battery, spark plug and HT coil) but you need to know what you're doing.

Are you prepared to go this far?