If you are new to World of Warcraft (WoW) and search around and ask other players what the best ways to make gold are they will likely tell you to get some gathering professions. Now while I do not really think that any of the gathering professions are the best ways to make gold you can make a lot of gold with them. You can especially make a lot of gold with mining.
Mining is a gathering profession skill that is easy to level up and has a high pay off. Crafting professions like jewelcrafting, blacksmithing, and engineering create a high demand for mining materials and allow miners to make lots of gold selling ore and bars on the auction house.
If you are taking on mining solely for making gold you can simply level your mining up and sell the mats in the auction house as you go. You will not make a ton of gold off of the low level supplies but they will sell. This is due to the fact, as I said above, engineering, blacksmithing, and jewelcrafting all require mining materials and anytime someone levels one of these professions that they need lower level mining supplies.
Making gold with mining is really simple, you only need to go out and mine for ore. I would recommend that you farm for higher level ores like saronite ore and titanium ore in order to make the most gold for your time. Once you have ore to sell take a look (you should be doing this pretty frequently to see how much mining mats are selling for regularly) at the auction house and determine whether or not you will smelt bars or sell ore. You will have to watch the auction house regularly as I previously said, to ensure you are making the most gold per stack of orres or bars you are selling.