These are just a few, off the top of my head!
I don't know what kind of necklace you're considering. Simple stringing is pretty easy. You'll need the stringing material. It's a coated wire made of many tiny strands. If you go with a higher number of strands it'll drape nicer. I use 49-strand Soft Touch. But it's more expensive, so if you're just starting, you might want to go with a lower count. You'll need beads, a clasp, and some crimp tubes. I recommend tubes instead of crimp beads, b/c sometimes the curvature from the crimp beads can cut/damage the wire. You can use some needle nose pliers to squeeze the crimp tubes closed as a beginner, but if you continue with this hobby, you might want to invest in some crimping pliers. It will give a more finished look. When you're crimping/finishing off your necklace, DON'T try to make the beads as tight as possible. If you don't have any slack, the necklace will not want to drape nicely. It'll be too stiff. That was one of my problems when I very first started.
There are other ways to make necklaces, too. I hope you have lots of fun making jewelry. It can be very addictive! Best of luck!
Fire Mountain is a great starter site. Tons of information and videos. They also have a section with designs. I would get my starter beads from old necklaces or craft stores. Theirs are lovely but they can be pricey.
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