Capacitors are removed from the board using heated tweezers where possible in order to avoid damage to the pads. Where there are restrictions due to space, I would normally use two small soldering irons or very occasionally hot air. I NEVER use a pair of pliers to twist the capacitors off – despite many YouTube videos showing that as a recommended technique it almost always causes damage.
In this case there is corrosion under the capacitors that has completely rotted through one of the pads. This shows up most clearly after cleaning.

In this case I use a small length of wire to bridge the connections and make a suitable pad equivalent to fix the new capacitor to. New capacitors are then soldered in place (in this case these are Polymer capacitors). Finally the area around the new capacitors is cleaned to remove excess flux.