Videos are much harder than still images. Some rather fancy cameras allow you to choose a specific frequency for sampling frames; for others you may have to use a long exposure time and cross your fingers.
You can also do it with the built in camera app on the iPhone. Make sure the "Live" icon is enabled. Then later when browing the photo, select "Live" in the upper left corner and then "Long Exposure"
These are my rules of thumb: For photos of CRTs, turning down the brightness and taking the shot at a side angle can help bring out the detail. Video wise, make sure your camera won't keep refocusing when the brightness of the screen changes during use.