This is going to cover some of the basic stuff. If you've got a pile of cash you can just go through the Centaur Forge catalog and order what you want, but if you're like me you have to pick up some basics and over time either buy or make other tools you need. So let's see:
Anvil. Obviously, you need something to pound on.
Forge. Also obviously, some way to heat the metal.
Hammers. That is indeed hammers, plural, you're gonna need more than one. I'd suggest a 2 or 3lb double-face or cross-peen, a 1 or 2lb ball-peen as the most basic to start with. If you work any heavy stuff, like flattening a spring, a 4lb is very handy. On the lighter side, one of the handiest hammers I have is a 24oz. ball-peen with a wider than usual face on the flat side; I found it without a handle at a flea market and for smoothing a surface or shaping some flat stock into curves, it's wonderful.
Chisels. Again, more than one. A heavy one with an edge at least 1" across for heavy cutting, smaller for more delicate stuff. Once you have the hang of heat-treating, chisels can be made from spring stock or drill rod or old rock drills, and over time you'll probably wind up with a collection of different sizes & shapes.
Punches. One good centerpunch for marking where to drill a hole, or where to make a bend; a punch for actually punching holes in stock. You'll learn to make other shapes and sizes as you go, and, again, you'll probably wind up with an assortment.
Tongs. This can be the tough one, because you've got to have them, but unless you find some at a flea market or antique store or something, you'll have to make them. You can buy them new(see Centaur above), but they do tend to be expensive. You can, for a while, get by with pliers or vise-grips, but tongs that will hold the stock well are not an option; if the piece can't be held solidly it'll move(harder to shape) or jump free(dangerous and/or annoying, but good for your dance steps). If you do much, especially if you make decorative stuff, you'll wind up with a number of them; they're not very hard to make, and in some cases it's worth it to make a pair that may only be picked up once in a while if they let you do the job more easily.
That's the most basic list you can get by with for a while. If you primarily make blades, a couple of tongs and hammers, a punch or two, may be all you need. If you make decorative and other ironwork, you'll wind up with more and use them all.
Tongs can have the jaws shaped specifically to hold flat pieces, round pieces, rectangular pieces(like the tang of a knife), and so forth. There's a style made to hold a hammer head while you shape it, and a variation of that for holding an axe head.
Punches can make a flat depression, leave a round-bottomed mark, leave special shapes like letters or symbols, and so forth. Chisels can make a flat cut, a curve, and sharp angle.
Hammers can have two identical faces, or two radically different ones; some old smithing hammers, and some specialized ones, have only one face that's used to strike with. I once read of a man who made decorative ironwork who had 49 hammers, each a different size and/or shape, many for doing one particular thing.