There are four basic tools that you will need for beading and jewelry work. These can be bought online, in bead stores and sometimes in hardware stores. From left to right:
A Flat Nose Pliers, the jaws are long, thin and flat where they touch against each other. I use them primarily for manipulating the wire.
Next, Round Nose Pliers, the jaws are short and round, and they go from thick (where they meet the pivot joint) to thin at the end. They come in different sizes, I like mine to be very very small at the tip.
Diagonal Cutters are... used for cutting
Crimping Pliers have been designed specifically for closing crimps, and have two notches in the jaws. These are to be used sequentially to create a secure crimp bead.
Wire: Both basic types come in several sizes and flexibilities; you may also use alternative materials such as elastic, ribbon, cord, etc.
On the left, beading wire; it consists of several very small strands of steel wire, wrapped around each other and coated in nylon. Good for necklaces, bracelets, etc.
On the right is sterling silver wire. It can be used to attach beads, make eyepins, headpins and jumprings, or to make into shapes.
Findings are things that help you assemble, hold together or attatch things to one another.
Clasps: Toggle Clasps: Consist of an "O" shaped piece and a "T" shaped piece. Once you slide the "T" part into the "O" part, the weight of the jewelry exerts enough tension to keep the clasp from undoing.
Connectors: Headpins: Are pieces of wire that have an end with a flat head, so as to stop a bead from sliding off. You place a bead and then do a loop or a wrapped loop (my preference) to secure the bead.
Connectors: Eyepins: Are pieces of wire that have an end with a loop, so as to stop a bead from sliding off. You place a bead and then do a loop or a wrapped loop (my preference) to secure the bead.
Earring findings: are the pieces that hold a piece of jewelry to one's ear. There are (clockwise from bottom left) earwires/french wires; lever backs; clip ons; posts with loops and flat posts. Each kind has it's own application, and are to be considered a design choice. Some earring designs look better with a post than a frenchwire, some earrings can only be made with flat posts.
Now that you know what things are called and what they look like, you can begin to learn some basic techniques!