Oasis cubes are one of the better rooting media available. But other media can work as well. At the grower that I work for, we use a polymerized soil plug as well as a soilless mix to start plants and cuttings in.
The biggest factor is controlling the moisture loss from the cutting until the roots start to form. Until then, the cutting can not uptake any water.
Two node cuttings are the most popular, like this...
Within each node of the plant are auxins that can produce roots. Actually, each cell within a plant has the ability to grow roots or shoots.
If you're going to dip a cutting into a rooting hormone, first find out if it's needed. Some plants need the extra help, others dont. Also determine what kind to use, either alcohol based or water based. I dont think peppers need the hormones.
The best time of day for cuttings is when the plant has been well fed and towards the end of the day. During the day, the plant is storing carbohydrates. It was once thought that the morning is the best time. New research now shows that afternoon is better because the plant uses a lot of the energy saved throughout the day at night.
New growth is typically better used for cuttings. In the picture above, you'll see two nodes or branches above the plug and a stem below. That stem went all the way down to the next branch and cut just above it. By doing it that way, it does not leave a dead stem above the node that will only just rot anyway.
Hope this helps.
Oh, when I get home after work today, I'll go through my books. I believe one has a section on pepper cuttings.
