Stone setting in general is much more difficult than many might suspect. There are short courses in various types of jewelry work but those provide only a basic starting place and years of experience needed to become truly proficient in many areas. Fortunately, if a person devotes time to stone setting and does enough of one style of setting to become comfortable with it, moving on to similar styles is not nearly as difficult as those "first trials".
As you probably know, stone setting is done in many different styles. Within those styles, one jeweler may use slightly different methods than would another jeweler doing the exact same job. There is room to experiment with methods but only after you have set a few stones and are pleased with the results. Once you have a feel for the metal and the gems, then you know enough not to totally mess-up by trying a slightly different method.
Stone Setting Styles. I will mention a few styles and recommend what I believe is the best place to begin.The prong settings using faceted stones. This is the best place to begin. Start with a round stone, sometimes 4mm to 7mm in diameter. Smaller stones are more difficult until you learn the "give and take" of the metal, while larger stones present other problems. Start with normal prongs, generally four or six to the setting.
There are lots of prong settings with fancy formed and decorated prongs but those are not the best with which to begin learning. I do not care if the prong settings are part of a pendant, ring or earrings. The idea is fairly plain and basic prong settings regardless of the jewelry type.
The Bezel Settings, is use a narrow area of metal around the girdle or waist of the stone to secure the stone in the setting. The most basic form is seen in typical southern turquoise jewelry, essentially a band of silver wrapped around the stone and press down toward the stone from the top.
The more dramatic and much more difficult bezel is "flush set", where a gemstone is set directly into the surface of metal such as on a ring band and the metal is burned or hammered to the stone then finished for smoothness. This last technique is quite difficult for a beginner and is best left until you feel ready for it and have the equipment to do the job.
Channel Settings. You have seen these settings in which rows of stones are set into a "groove" or channel of metal. This is also a difficult job and should not be attempted to start. To try a channel setting without lots of previous metal and seat cutting experience will lead to frustration and disappointment. Look at channel set stones at a jewelry store.
Inexpensive jewelry is a "fake job" and the stones are in a channel but held in place with little burs of metal pushed over opposite sides of the stone. Stones fall out of these settings! A real channel set has the metal along the channel pushed down onto the stones, all along the channel. You need to learn to bezel set before doing channel settings since some similar techniques are used.
Bead Set or Pave Setting. This setting is done with hand tools in the final stages, forming metal over one stone at a time and sometimes two at a time using "graver" tools. This is advanced technique. A setting style with a similar look uses "needle point" prongs formed to start with in the metal. We can talk about that sometime down the road.
Fancy Shaped Stones. Even when using prong settings, fancy shaped stones need added techniques. Essentially the same methods are used to cut seats and tighten prongs for emerald cuts as for round and oval stones. Marquise and pear shapes have a pointed end requiring a different seat cutting method to hold the pointed end securely without breaking the stone! The problem with emerald cuts is getting the stone level and straight and secure enough that the stone will not "turn" in the prongs.
The problem with stones with pointed ends or corners is cutting the seat and tightening without damage to the stone. Such fancy shape are not to be scared but understood to be more difficult, requiring practiced hand control before attempting.
Settings. I recommend starting with simple prong settings, generally found in four and six prong versions. Note, jewelers often use the words settings, heads, crowns and mountings to mean the same thing.
Stone Shapes. I recommend round faceted stones in sizes from possibly 4mm to 7mm. You may try ovals stone, too, but do a few rounds first. With ovals, over tightening any prong can make the stone go sideways a bit in the prongs.
Stone Kinds. CZ's are good to start as are man-made birthstones. Most of the birthstones are synthetic sapphire (corundum) and are quite hard. The value of these stones is, they are pretty when set and are not expensive. The cuts are fairly uniform, too, compared to less expensive natural stones. Still, you need to practice on some stones which are not as tough as the birthstones. For this, choose possibly some inexpensive, meaning almost colorless, amethysts and inexpensive garnets.
These will not be the most beautiful gems but are wonderful for practice and can look pretty in earrings and pendants. You will likely discover the girdle or waist of inexpensive natural gems may be varied in thickness and the angles of the facets on the pavilion or bottom of the stone may vary. The idea is to get the stone level in the mounting so it looks level to the eye.
For the work to be done just like it should, stone seats need to be cut into the prongs to match the gemstone on hand. I suggest trying something in sterling silver. The metal is easy to bend and work. In fact, sterling is soft enough to "over bend" without due care. Gold is somewhat more springy and takes more effort to properly set than silver. However, gold is more forgiving than silver and certainly takes a better finish in the final steps. I suggest a sterling pendant, facet set stone in prongs. That is a good starting place.
Please, keep in mind the main idea is to have a finished piece that does look good to the eye! The stone should be safe and secure in the setting but that is not "seen". What is seen is the finished jewelry. That is the impression both to you and to anyone who happens to see it. Set the stone at a pleasure depth in the prongs, stone set level, finish off the prongs so all is uniform and neatly done. It will take some time to get use to this kind of think, but when you do get to use this kind of thing you will have no problem fixing your jewelry, your families, maybe even some of your friends jewelry.