Rubber gloves and disposable dust masks (available from any hardware store). Old clothes or a smock to avoid stains.
A word here about the future if and when you move on to other types of dyeing. Don't generalize the simple safety procedures and equipment we use with innocuous MX dyes to other classes of dye. Working with some types of dye will require special procedures, special gloves and goggles in addition to a dust mask or respirator. Be sure you review pertinent safety precautions!
It is necessary that you have a special set of measuring tools and containers just for dyeing. Store these where whey can't be mixed up with your kitchen equipment. Garage and estate sales are immensely useful for acquiring such things.
Watch for measuring spoons and cups -- these don't have to be complete sets. I find 1/4 and 1/2 cups and 1 teaspoon and 1 tablespoon most useful. You may want to watch for pint and half-pint canning jars (to hold your dyes); I used to do this and it was such a pain to wash them and buy rings and discs that now I just buy them new by the dozen from Wal-mart for $7.00 or so; of course you can reuse them over and over (ONLY for dyes, please).
Particularly important are glass bowls and casserole dishes (to soak your floss in dye activator) and glass cake pans (to keep your plastic-wrapped dyed floss warm while it "cures"). It doesn't matter if these are chipped as long as they're not dangerously sharp.
Above: Floss soaking in a glass loaf pan of dye activator; half-pint and pint canning jars holding my dye working solutions.
Look also for small glass custard cups (to mix dye colors) and for big bags of plastic spoons (people keep these surprisingly often, then get tired of washing them).
Veteran garage salers will realize that one doesn't find all these things in a single afternoon. Keep an eye peeled, and alert your garage-saleing friends to your needs.
You'll want a roll of paper towels at hand and good clingy plastic wrap for wrapping skeins after dyeing.