First of all, get rid of the spikes. Just keep the cacti in the flowering pot while you use V-cuts to take away the spikes. You can also use pliers (but the spikes have to be removed together with their roots).
After removing the spikes, you can start slicing the cactus into pieces. Cut the pieces 1 cm thick slices.
Prepare a cooking pot with water and add lemon-juice or ascorbic acid to the water. The ascorbic acid (which is also present in lemon-juice) enhances the solubility of the alkaloids.
Put the slices into the water and let them cook for several hours (generally 7 hours). Never let the pot out of your sight. Because the water will vaporize, you’ll have to add some water several times. After 7 hours, filter out the remaining plant material.
Keep the liquid cooking until you have about 2 mugs of liquid left. If you don’t have that much time, you can also put the plant material (without spikes) in a mixer.
Prepare the water as described above. Now you only have to cook the cactus slices for 2 - 4 hours.
Filter the plant material by pouring the content of the pot into a dish towel and squeeze the remaining liquid out of the plant material.