We just watched a video yesterday on the correct way to apply TED hose. We didn't actually get a chance to apply them to anyone or anything, as we were moving quickly on to physical assessments (head to toe). But here's what I remember from the video.
The hose come with a tape measure, for measuring the pt's leg circumference. Nursing stations always have one tape measure one hand, and since you need to measure the patient's leg BEFORE opening the package, get the tape measure from the nursing station to use on the patient. Then, when you get the correct size, return the new tape measure from the patient's package in place of the one you used from the nursing station.
Now, as to applying them.. The person in the video kind of placed them over her arms, all the way to her hands first, and then pulled them off inside out all the way down to the foot area. grasping the inside of the stocking with her thumb and forfingers, she slid this part over the feet first, and then pulled up from there, small sections at a time.
Hope this helps, although I think wsiab's suggestion looked easier!