The 6080 King’s Castle featured a full dozen minifigures and I am scrambling to find parts for as many of them as possible from my old LEGO collection. Since the 1980s LEGO Castle used various different color combinations in minifigure parts, I am lacking things like red legs with black hips, while I do have several all red and all black minifigure pants from other LEGO sets. As for torsos, there too I might have the correct minifig shirt from some other castle set, but with incorrect sleeve colors. Luckily limbs can be swapped.
The Ugly Duckling does a better job at describing the entire process, but to cut a longer story short: Minifigure arms come off by raising the arm in question forward and then, with your thumb, slowly bending towards the side from the armpit, while holding your index finger behind the arm to keep the motion slow. You will notice when it starts to come off. Hands can also be removed, simply by pulling them out. Minifigure legs are removed by raising one leg out of the way to kicking position and then pushing the other straight leg directly to the side. Pushing legs out takes most force of the three. Unlike with arms, absolutely don’t bend minifigure legs when removing them.
Keeping the torso and the pants attached to each other during arm and leg removal helps in holding the minifigure, just make sure the arms are not blocking the legs when removing legs (raise the arms up first). You can do the removals without this help, but it will be harder. I would recommend removing other parts like the head and accessories beforehand, though. And while none of this is black magic, there is always a risk of breaking the minifigure in the surgery process. Several surgeries may also loosen the parts. Take care, you have been warned. The reverse is fortunately easier: Replacement of arms, hands and legs is done by simply pushing them back into their respective places.
Last but not least, I’ll mention some black magic that will definitely risk and break bricks. TLG produces keyrings and magnets that feature metallic chains and glued (or otherwise permanently bonded/attached) minifigure parts. You can see one older example on the right above, it is a 1980s LEGO Castle keyring that I probably brought from a trip to Legoland in Billund, Denmark. The helmet, head, torso and hips of the keyring are fixed, only the limbs move. More adventurous people have disassembled similar LEGO keyrings and magnet figures for parts, see e.g. The Brick Blogger here, here and here.
Apparently the melting point for ABS plastic (the plastic used in most modern LEGO pieces) is 80 degrees Celsius, so soaking in 71 degree water for five or more minutes may separate certain bonds without damage. The Brick Blogger warns against moving the limbs of warmed minifigures before cooling, though. Unfortunately not all LEGO pieces and keyrings are made of the same plastic. Also, there may be many types of bonding out there.