How do I measure startup/inrush current?
LittleFuse provides a very nice app note with a lot of details for the design of these kind of devices.

As for measuring the current, you could use a very small resistor (1 or 0.1 ohm resistor) and use an oscilloscope to measure the current. Be careful not to ground the device. You need to use two probes for doing this measurement and subtract the value of one from the other - DO NOT CONNECT THE GND OF THE PROBE TO EITHER SIDE OF THE RESISTOR- you will in effect cause a short circuit if you do this. Just get 2 probes, connect the tip to each side of the resistor, and the grounds to the actual ground. use oscilloscope math capability (or just yourself) to do a difference between the two channels and this will be your current.