Ah, an easy job. With the colder weather my passenger door was drooping quite a bit when opened, so it was time to replace its lift piston, aka door strut.
Every vendor sells door struts; I got mine from PJ Grady. These last a few years before they wear out and need to be replaced. Replacement only takes a few minutes. The main trick is that the door is really heavy, and the clips can be a little fiddly.
Propping the Door
The first thing you'll want is a piece of wood to prop the door open. It weighs quite a lot, and you don't want to have to hold it up while fiddling with the struct. I used a 2x4 that happened to be just about the right length to keep the door most of the way open. Make sure it's stable, as you don't want the unsupported door whacking you in the head.
Removing the Old Strut
The struct is locked in place with two clips that slide through small holes in the ball sockets on the ends of the struct, then rotate around the strut to securely snap into place. Simple pop the clip up away from the struct, and then side it away from the socket to remove the clip. The new struts should come with new clips, but it's best not to lose the old ones, just in case.
Even without the clips, the strut will stay securely on the door. Don't think that you don't need the clips, though; it's entirely possible that the struct could pop out and you'll suddenly have the entire weight of the door dropping on your head.
With the clips out, you can remove the struts. Hold the door as high up as you can and give the top of the strut a solid hit with your hand towards the back of the car. If you hit it hard enough, it will pop off the ball on the door. You can now rest the door back on the support 2x4, then simply tilt the top of the strut towards the front of the car until pop it off the bottom ball.
Installing the New Strut
This is another simple process. Which side of the strut goes on which ball seems to be pretty arbitrary, but I put the wider part near the top.
I started with the bottom of the strut: simply rest the socket of the strut against the ball on the body, and then give it a firm hit with your hand, and it should pop into place.
At this point I'd recommend putting the clip in the socket, before attaching the other end of the strut to the door. You can rotate the strut so that it is pointing away from the car to make it much easier access to the hole that the clip has to slide through. It is important that the clip slide all the way in. If it doesn't, you may have to rotate the socket relative to the ball a little so that the holes aren't being blocked by the ball. Once in, rotate the clip around the arm to lock it into place.
Once that bottom is installed, you can swing the strut around and pop the socket onto the ball on the door. You'll likely have to lift the door with your free hand to line up the ball and socket, and then either firmly strike the strut with your hand or simply pull the strut towards the ball until it clicks into place.
Again, the clip goes into the hole on the socket, although this time it will be underneath instead of above. You again may need to twist the socket relative to the ball to get everything lined up. Once the clip is all the way in, you can rotate it around the strut body to lock it into place.
Now you're all done -- you can remove the 2x4 or whatever support you were using and operate the door as normal.