The main method used to buy and sell items in WoW is the Auction House. There are worldwide trade channels that you can use but these are nowhere near as important as the 'AH'. You can only learn how to make gold in WoW without farming if you take the time to master the AH and there is a lot more to it than just posting your stuff for sale at the lowest price.
Buy Low, Sell High
You can make gold in WoW without killing a single mob or learning a single profession if you know how to 'play' the auction house. This is basically the art of finding items that are cheaper than market value, buying them and then immediately reselling them at a profit. You make gold without even leaving the auction house. That means that you can even create a low level character to be your auction house character and have this character do nothing but make gold for your main.
Finding Items to Resell
There are thousands of items for sale at the AH at any one time. So how do you find items that can be resold at a higher price without spending hours searching for them? The answer is the Auctioneer addon. The SearchUI module of Auctioneer can be configured to find profitable items automatically. The addon is available from the Curse Gaming web site. Auctioneer is an absolute must for anyone who wants to learn how to make gold in WoW
Convert and Disenchant Items
If have a character with the enchanting profession, you can also use this to 'play' the auction house. Auctioneer will tell you if an item can be disenchanted into a shard that will sell for more than the purchase price. Your auction house character doesn't need to be the enchanter. You can always mail the item to another char, have them disenchant it and mail it back to you. There are other ways that some items can be converted for a possible profit. For example, greater shards can be converted to multiple lesser shards which might actually sell for more in total.
Control the Market
Advanced auctioneering involves controlling the market for certain items that you sell. For example, if the market price of an item is lower than usual, you can buy up the cheaper items to push up the price. Or you can buy all of them and set whatever price you want...as long as customers will pay it.
Playing the auction house is not only profitable, it can be a lot of fun too and with a little practice and the help of Auctioneer, it can make you rich without farming or professions.