Current input of discmans and walkmans
You measure the current using a DMM (digital multi meter) on a current measuring scale. When making the measurement it can be best to use brand new batteries because the higher voltage may increase the current drawn by the circuitry. In some cases where newer types of devices may contain a switching power supply for voltage level conversion you may also need to check the current draw on a battery that has been used quite a bit and may exhibit lower voltage.

If the device uses standard type batteries such as AA or AAA in a battery compartment one way to conveniently measure the current is to make up small thin assembly that you can slip into the battery compartment between one end of a battery and the compartment contact or spring. This thin assembly needs to have conductive metal on each side that then attaches to a pair of short wires, one on each side, that can extend out of the battery compartment for attachment to the meter leads. 

A simple scheme would be to use some heavy paper card stock and glue a piece of aluminium foil on each side. Make this the width of a battery but about twice as high. Once inserted into the battery compartment you could simply hold the current meter probes to two sides of the assembly so that the battery circuit is completed through the meter.