You'll need about 3 to 4 feet of fine wire, 199 seed bead (plus extras in case you lose a few) in at least 2 different colours (I usually use 3-5 colours), and a pair of scissors. These are sold at numerous art supply or craft stores.
Step 1: Materials & Getting Started
First measure yourself two arm's lengths of wire, which should be way more than enough, especially since you will be using seed beads. It has to be thin wire, fine enough to fit through the beads you are using at least twice. It's better to use too much wire than too little. Too much, and you can use the excess to make the wings or to connect the dragon pieces together. Too little and you need to start over.
You'll need 199 seed beads. Those are those really tiny little beds about a millimeter wide each, though sizes may vary a bit. You can pick these up in most art supply stores. Though the dragons consist of 199 beads apiece, you will need more than that, A. because you probably want an assortment of fun and funky dragon colours, and B. because you will almost certainly lose a few beads while making the dragons because they are teeny and lightweight.
Have a pair of scissors handy too, for cutting the wire.
A. String two beads on the wire. MAKE SURE they fall to the center of the wire.
B. Now string two more beads onto wire A (see picture) and CROSS wire B through those same two beads in the opposite direction. Your wires should cross inside the beads and emerge from different sides.
C. Pull the wires tight. Congratulations! You've created your second row!