I've propagated a lot of prickly pear. They root easily and grow roots faster than most cactus. You could just stick it in soil a few days after cutting, forget about it, and it will most likely grow roots.
That being said, it's best to give the cactus more than a few days for the wound to heal, a fresh cut is more susceptible to disease or fungus. I usually wait a week or two, until you can see the color of the inner flesh turn more brown and recede. After the cactus has healed enough to avoid infection I plant the cutting in well draining soil enough so it can support itself. Though you may need to
get a stick from your yard or a pencil and support the cutting on both sides. Then place the newly potted cutting in indirect or limited sun for a month or two. Most of my cutting are growing roots by two months. If it's outside do not water, and if you live in a rainy place then I would bring it in during storms. If it's inside you can water once a month. At first there's no roots so no need for water. Taking a cutting that is already showing new growth is a good indicator that your new cut will root quickly. Keeping the soil warm (~70 °F) also encourages root growth.
How do I know that it's ready?
You will see the inner flesh callous and recede. Later, you can check for roots by giving it infrequent, very slight tugs over time and you will notice when it begins to root. (Doing this can damage early roots, don't do it often)
Will I see roots appear at the bottom if I leave it in this position for some time?
If you keep it somewhere with minimal light you will eventually see roots begin to grow, but results are always better for me when I plant a cutting as soon as it's healed. I've noticed roots will also grow from the areole also.
Do I have to humidify the soil a little so that the roots can grow?
Once it's planted, do I have to wait a few days/weeks before watering it for the first time?
Since you mentioned inside, I would give it a light watering after planting and than monthly after that until it's rooted. Remember they don't have roots, so they don't need much water yet. As soon as you have roots growing, water as expected for your location and time of year, etc.
