When the car is off the ground, the strut is at maximum extension. The spring still has some "spring" left to go, but it's being contained by the strut, strut assembly, and the strut mount.
With the car off the ground, remove the nut that holds the tapered fitting, then break the fitting free with a pickle fork. Next remove the bolts from the bottom of the strut mount. Push down on the control arm, and the ball joint might drop right out. If it doesn't, rap it a couple of times with a hammer, and you're set.
Now honestly, I've never changed the ball joints while the strut assemblies were still on the car. I did them while I had the strut assemblies off (changing the strut inserts and springs). But the way I re-installed everything (both times) was by inserting the strut mount (top) into place, hand-tighten the nuts, then line up the ball joint to the control arm. At that point, we're talking about the same procedure I just outlined for changing the ball joints.

Jeff Pierce
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'92 Mercedes 190E (my daily driver), '93 945 Turbo (a kickass family car), '53 Willys-Overland Pickup (my snow-plow truck/conversation piece)