Dry:

1.  Letting the cactus cutting dry in indirect, diffuse light with good air circulation is important. The larger your cutting is the longer you should wait for the cut to heal. Once the wound is completely calloused over, it is safe to plant directly in soil. Generally, 1-4 weeks is good practice. If uncertain, giving the cactus cutting added time to heal is best practice. 
2. Container: Find a pot suitable for the size of the cutting. Aim for an equal width to depth ratio. The width of the pot should be relative to the size of the cutting. A pot with 2x the width of the cutting is good measure.
3. Soil Plant the cactus into any readily available cactus mix to a depth of at least 1/6 the length of the cutting. A good Cactus Mix is ideal, but most generic cactus soils can also work ok for Trichocereus spices cacti. DO NOT WATER, DO NOT LEAVE IN DIRECT SUNLIGHT UNITL NEW GROWTH APPEARS.
4. Roots: It will take a number of weeks for the cutting to grow roots and become fully acclimatized to its new environment. During this critical time, it’s important not to expose the cutting to direct sunlight, not to water, or have extremes in temperature. Keep in mind the rooting process will take significantly longer in the winter months. It is recommended to root cacti during their active growing period. Be patient, the time frame is at least a number of weeks.
5. Growth: Once new growth is evident through lighter shades of green around the tip or with the emergence of new stems etc. it can gradually be exposed to full sunlight and watering can slowly begin. Your cutting is now a self-sufficient cactus ready for normal atmospheric conditions.