Is there a specific technique, or something, for wrapping a stone with wire for use in a necklace? Is this just a freeform type of thing I can do myself, or is there a special way of wrapping?
Wire-wrapping a stone is a freeform technique that utilizes your own personal creativity and tastes for each design. The recommended wire for ease of wrapping is half-hard 22-gauge round wire.
Half-hard wire offers a good combination of malleability and durability making it easy to create a bend in the wire and have confidence the bend will stay as you made it. The gauge is delicate enough to not overpower the stone you are setting yet substantial enough to hold the stone in place.
You may find your design would work better with a heavier wire, such as 18- or 20-gauge wire, or a finer wire of 24 to 26-gauge. You may personally prefer working with a wire that is more malleable, like dead-soft, or more rigid, like full-hard. These are all options worth experimenting with as you develop your style and design repertoire.