Recognizing of broken capacitors is not so simple in some cases.
Sometimes (very often in my case) have capacitor its nominal capacity but it has high serial current. When you connect DC voltage of capacitor nominal value and capacitor have some serial current throught it, then it is broken. Only charging current is allowed (short current peak on connect).
Sorry for my english.

Good article. I have personally made this repair sucessfully many times using only a basic hand held solding iron and hand held desolder pump.
Like you say the motherboard sinks away the heat fast. You need an iron with between 70 and 100 watts and a large flat tip. If it spans both solder points of the cap its really easy

Just heat and gently pull the cap out from the other side of the board. Then clear the holes with the heated pin method or use a desolder pump. If you heat the hole on one side and use the pump on the other side it should clear easily.
Only other thing to note is. Be QUICK, practice on some junk board first, you dont want to burn a big hole in your board or lift of the tracks.

Im sure most people don't have a professional solder/desolder station. These cost at least $160 usually more.

Another trick. Assuming the old caps are dead and of no further use. Pull them off thier leads.
If you pull a electrolytic capacitor hard the leads will pull straight out of the body of the cap.
Leaving just the leads sticking up. Its now much easier to remove becuase you can desolder the leads and remove them one at a time.