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Professions vs. Farming vs. Hunting
If you are a goblin or have guild perks, the costs are a bit lower.
Level 20 - Ground mount
Apprentice Riding total cost: 5g
This one is super fast to obtain, even if you have 0 copper to start with. You'll earn so much gold from the following tricks that you'll have enough for your second riding training aswell as flying training on top of the initial level 20 mount, especially if you perform them all.
You often have to wait a bit if you use only auction house to sell your stuff. But if you sell them in trade chat instead, you don't have to wait for long and auction house won't steal part your golds.
Low level trade goods are very popular, so they not only sell fast, but often also for a nice chunk of gold aswell. What to farm depends mostly on what is expensive in the auction house. Search the trade goods category and filter the higher level goodies from the list.
It's usually a good idea to farm herbs, ores or cloth at any given level. If copper ore sells for 1g each, you only need to mine 5 ores and you have enough gold for your first riding training and mount aswell.
Skinning: Is a very good low level gold maker also. Most low level leathers sell for 1-5g each!
Fishing: You may also want to give fishing a go if certain fishes are expensive. It's often enough to find a larger pool of water and run along the shore until you find a shcool of fish. No matter what kind of fish it is, you're bound to make a few gold pieces every minute.
If you don't know where to farm a certain item, do a search in Wowhead.
Inscription & Alchemy: A scribe can make glyphs that sell for 10-500g each, even the low level ones. Vanishing powders also sell fast. You do need to obtain some herbs first though, so herbalism is highly recommended as a second profession. Same goes with Alchemy, except low level potions don't sell that good so it's not a good choice often.
Treasure chests: Almost all level 10+ treasure chests contain blue quality items. These can be sold for 20-150g each, more if it's exceptionally good for twinks. Treasure chests will appear on your map if you use Gathermate 2 addon, so it's easy to see where they are to be found.
Raptor nests: Certain zones have raptor nests that once looted, give you a raptor companion pet. This can be sold in the auction house for 70-1000g, price depending on if anyone else is selling it. To see where they are located, check the map found here.
Reselling pets/recipes: The above map also contains other pets that can be sold in the auction house. You might also want to buy cheap recipes from vendors and resell them in the auction house for even 20-500g more.
Reselling vendor items: If you have a few silvers already, you don't even need to leave a city if you follow the tricks found in this post.
Level 40 - Epic ground mount
Journeyman Riding total cost: 60g
The above methods should make you 60g in no time.
Level 60 - Flying mount
Expert Riding total cost: 300g
There are no level 60 specific methods of making gold, except jewelcrafting starts to shine at these levels and you have access to few valuable trade goods.
Fel Iron ore is extremely valuable, and so is Felweed. These can be both found in Hellfire Peninsula, Outland. Though it would be more wise to farm these only after obtaining your flying mount.
Jewelcrafters can invest some gold at these levels by buying thorium, mithril, fel iron, adamantite or iron ore. Or if you have mining, get the ores yourself instead. Often a stack of above ores can get you 50-100g when prospected. Check the gem prices on your realm first though. If you're not sure what gems can be obtained from a certain ore, do a wowhead search again.
Level 70 - Epic / Cold weather / Master / Old weather flying
Level 70 epic flying total cost: 5100g
Cold weather flying total cost: 500g
Master Riding total cost: 5000g
Flight Master's Licence total cost: 250g
At level 70 you have access to almost every method found on this blog, and they all should make you even 50000g in a day if you try even half of them.
If you don't want to waste much time, there's also this new automated gold making addon that claims to make you 999999 gold in 30 ish days, also known as hitting the gold cap! :)
Did I miss your favourite way to make gold for a mount? Let me know!