Hi Kevin,
There are a couple of different ways to determine how fast a "solar storm" is moving. One way is to use what scientists call "in situ" measurements of the solar wind. Basically, this means we use data from instruments on a spacecraft that directly measure the speed of the solar wind plasma flowing past the spacecraft. Here is an exercise to help you understand how a scientist might figure out how fast a solar storm is moving using this type of data: http://image.gsfc.nasa.gov/poetry/workbook/page6.html
The other way a scientist can determine how fast a "solar storm" is moving is to compare the size and shape of the CME in a series of images from a satellite like SOHO. You might call this a "remote sensing" technique because it uses observations of something made from far away, rather than directly measuring the parameters. Basically this involves understanding the scale of the solar images, or how much real distance in space corresponds to a given length on the image of the Sun, and knowing how much time has passed between each of the images. Here is an exercise you can do showing how this method works: http://sohowww.nascom.nasa.gov/explore/lessons/cme_activity.html
Kris