As has been said, what do you mean by real? Technically anyone who wants to go out, shape some metal, wrap a handle on it, and stick it in a scabbard can call it a sword. So then the argument comes on quality.
Doing some initial research on katanas will help first off. Both Wikipedia and Howstuffworks have some great info on Japanese sword history and the evolution of the katana. Search around those sites and you can find exactly what you're looking for.
When you go to buy one, what do you want it for? If you simply want it for decoration then just about anything will do. If you're wanting to add it to a collection then you're going to want to get a blade with some age on it and those don't come cheap. That will also take some additional research into swordsmiths so you can identify authentic blades from fakes ( prominent smiths often "signed" the tang of the blade. ) If you just want a quality katana with solid construction and traditional crafting techniques, you've got a good selection and a broad price range before you. What you want to look for is a differentially tempered hammer laminate ( folded ) blade. The folding allows the metal to retain strength but stay light ( because it can be thinner. ) The differential tempering happens by packing the edge of the blade in clay and then tempering it edge down. The clay retains heat and makes the edge cool faster than the back. This allows the edge to be hard so it can receive and keep a keen edge. At the same time the back will be softer so it can absorb impact without breaking. This will also result in a hamon, that wavy line that runs the length of the blade between the edge and back. The furniture is up to your personal taste in what styles and colors you want: brass, bronze, steel, whatever. Traditionally the hilt was attached by one or two pins through the tang, wrapped in stretched ray skin, menuki were put in the pins, then the cord to top it off. The scabbard was lacquered wood. The same things will apply to the wakizashi and tanto. And while the katana was was the main battle weapon, the wakizashi was comparable to a Western officer's sidearm. The katana was left at the door while the wakizashi was always worn ( and usually kept under or beside the pillow during sleep. ) The two together were referred to as the daisho, or big and small. So if you want to complete the look, you'll need both.
Any quality blade will usually give details in the construction process. Cheaper ones usually don't mention anything on it. As long as you look for these basics, you should get a pretty good blade. On average you'll spend $200 - $350 on a good quality sword but prices can go above $1500 for a fully handcrafted wootz hammer laminate blade.
Museum Replicas Limited usually has a good selection of top quality, combat ready replicas. I've purchased stuff from them before and I've never been disappointed. Almost everything they offer is either based on actual museum pieces or known styles that actually existed, except things in their fantasy section.
If you need any other info, I'd ask RobT or Necronos, if you can ever find them online. They focus more on European swordplay, but I'm sure they can give you some good stuff.