First of all you need a pair of needle-nosed pliers. You could always steal a pair out of the garage and use those, but since they're made for things like bolts and nails (or whatever-- I'm not much of a handywoman) they're really too big for what you need to do (although they'll work in a pinch). Places like Micheal's and Joann's sells pliers for beading with their beading supplies. If you're going to do a whole heck of a lot of beading, you'll want to buy a higher-end pair, because they'll last longer. But if, like me, you mostly intend on doing repairs or only need to use them a couple times a year, the cheapest ones they sell will probably do you just fine.
Other tools you might find useful: a pair of tweezers (to hold beads) and a beading tray (so you can line up your beads pre-stringing). Since I do so little, I go without these two tools, but they can be useful.
Most of the money you spend on repairs will be on string, crimp beads, and clasps.
String first: there are loads of options on what kinds of string to buy. You can get elastic for stretchy bracelets, wire for earrings, natural fibers, or (my personal favorite for necklaces and flexible bracelets) nylon-coated wire. For a cheaper, similarly flexible necklace or bracelet, you can go with fishing line, but be aware that it will break fairly easily (don't use it for your pearls, fine metals, or other expensive beads!).
Crimp beads are pretty basic, and I've never met a crimp bead I didn't like. They are slipped on to the beaded piece right before the closure and then pressed closed with needle-nosed pliers to keep the whole thing together. Pretty important!
And, clasps. I know someone who replaces all her bracelet clasps with the loop-and-bar type as soon as she gets them, and does the same for her friends-- this ends up being most of the "beading" she does. Clasps can be cripplingly expensive, or super cheap-- entirely based on your preferences (I go cheap, because my preferences are cheap).
Anyhow, all this just goes to explain what I did the other day. My Mom delivered me a broken beaded piece:
This is how much line I had left over after re-stringing:
So to add the other half of the clasp, you have to string on the crimp bead, string on the clasp, and the re-thread the string through the crimp bead, which leaves a loop to hold the clasp in place. I start the process loose and then pull the whole thing tight after I have the thread through the crimp bead and several of the beads closest to the crimp (which hides the end). Then press the crimp bead tight (without breaking it!) and trim off any extra wire/string (there's a really good explanation of this with pictures here, as well as some explanations of some of the other ways of finishing a piece).
This is the necklace after the repair:
Pretty cute, right? (Mom assures me one of us made this-- it must have been her!)
I have plans later (like, when I have money, later) to re-string some of my favorite pieces from when I did a lot of beading. While I did make a whole lotta ugly pieces, some of them were actually kind of charming, so I'd like to make them wearable (figures that even when I did something right I would do something wrong-- they're all too small or on breakable uncoated wire or some such nonsense that means I have to fix them :/)
Till then, I guess I'll return to my knitting and sewing projects that don't cost me as much!