You can buy Japanese swords in many different places and from many different dealers: sword shops in Japan, sword shows in the US or overseas, gun and military shows in the US or elsewhere, eBay and other online auctions, postings on the For Sale forum on this message board, from other collectors, and from online dealers. Check the links at the top of this board 's home page and you 'll find a list of dealers with swords at a variety of price levels.
Finding swords to buy is easy; knowing what to buy takes serious study. Your first ten swords should be books. You should attend sword shows if possible and beg your way into collections to see and learn. Read, ask questions, reread, and ask more questions. Only with knowledge can you make an informed decision, and appreciate and understand what you are buying.
If you are ready to buy a sword but are uncomfortable with you level of expertise, you would be smart to stick with well established dealers and/or swords with authentication papers from one of the important sword societies in Japan. Even then you should be asking lots of questions. If you are still unsure, ask questions: From the seller, and from other collectors. Ask this forum. but ask someone, as once you have bought, it is too late to go back. Usually fellow enthusasts will be glad to assist and guide you through the process. Always run the dealership through an online search and see what other's experience of them was. You will never find total concensus, but most should agree.
It is a fact that you should always buy a sword in-hand and in person, and not from pictures online. This is good advice to follow, and is probably the most important advice you will get. But if you are unable to, then refer to the advice above, or delay the purchase until you can.