Here's a basic strategy for grinding gold while leveling up in WoW. It's pretty simple and I use it on all of my characters. I never have a problem buying my mount come level 40.

1) Don't worry about gear too much. Buy weapons for melee characters, but don't overdo it. You'll be gaining plenty of levels a week. There's no point in spending lots of your hard earned gold on some item that will be crap in a week anyway. Just get appropriate greens every 5 or 6 levels and make do.

2) Sell non gray items at the auction house. Nearly all of them will sell for more than what you'd get from a vendor. Be on the lookout for good pieces of gear with level 19 and 29 restrictions. Those are prime time pieces of twink gear. Lots of people like to buy their low level characters tons of great weapons and gear and let them dominate the lower level battlegrounds. I've been lucky enough to have a nice blue drop for one of my chars. I could have used it, but it was a really good piece of rogue twink gear, so I sold it for a good 50 gold :P To a level 70, 50 gold isn't much.

3) Pick two gather professions and sell the raw materials. I prefer mining and skinning, but some like herbalism. Make an effort to grind in areas with mining nodes and skinable animals. You'll make lots of gold this way. Sell the raw materials at the auction house. Don't bother turning the ores into bars, they sell better as ores (the exception to that is early on, do it to help increase your mining skill. As long as your mining skill is closed to max, sell the ores).

Those 3 tips alone should have you enjoying your mount at level 40 with no problem.

If you're interested in a guide that is packed with more information than you'll find anywhere, you may want to check out the World of Warcraft Cash Creating Guide.

I won't bore you with a huge sales pitch. You'll get plenty of that at his website, lol. Still the guide is really good and has plenty of ways to make 100 gold per hour or more. And as good as free resources (this site included) are, the information is read by tons of people, meaning all these gold spots become highly contested. I highly recommend you check it out to get a leg up on other players.

Here are some pretty nice spots to go in the higher levels.

Level 60ish
Western Plaguelands - Felstone field
-There are plenty of undead hear to farm runecloth.

Felwood - Jadefire Run
-Satyrs. They drop plenty of runecloth to farm.

Felwood - Pretty much everywhere
-If you can skin, the bears are very good gold.

Scarlet Monastery
-Just run through the instance. Decent drops and cash. Especially good if you can grab a hole bunch of mobs and AoE them.

Lvl 70ish
Nagrand
-Kill elementals.

Outlands Quests
-This pretty much doesn't need an explanation. They tend to give decent items and large amounts of gold. Shadowmoon Valley and Neatherstorm are particularly good.

Those are a few good spots I thought of off the top of my head, I'll add more later.

Here's a nice tip for low level grinding. I've seen it posted a lot of places, but it's still nice.

The mobs are around level 12, so it can be done very early. Head to Westfall and move near the coast. Overlooking the coast you will find a Windmill with Defias mobs around it. They drop some coin plus linen cloths. Their respawn rate is very fast, so this can be done at higher levels too. Kill them over and over again and sell the linen at the auction house.