dragonvale
The Air dragon is awfully expensive. I know you can breed it with an Earth dragon and a Sandstorm dragon or a Dodo dragon, but both of those require either an Air dragon or an Air hybrid dragon to breed.
Is there any (legitimate) way to get an Air dragon without dishing out 500 gems?
The only ways to get gems are to:
If you just started: At several points, the tutorial will give you gems and tell you to use them. Ignore the prompts, and you'll get to keep the gems.
There is no limit on how many gems you can receive from friends, but every player can only gift 3 gems per day (6 if they have the Dragonsai Gifting Tree). So generally you can get a maximum of 3/6 gems from friends daily - unless you can find someone willing to give you gems for nothing in return.
When you complete in-game objectives called "goals", most message pop-ups will have Facebook/Twitter sharing buttons. Use both to receive 2 extra gems. Some goals themselves also have a small gem reward attached to them.
The Colosseum will win you 0/2/5 gems per day. You can enter one dragon a day, and at most you'll get 5 gems per day back as a reward.
Winning the race gives you a spin of the prize wheel - rarely, you may win some gems. Entering the race is relatively inexpensive and frequently rewards gold, so entering hundreds of times per day is not out of the question, assuming you have enough time to devote.
Every month a rare dragon is available for breeding which matches the birthstone of the month. These dragons can only live on gemstone island. When upgraded to level 10, these dragons produce gems at a rate of 1/week. By default you can have at most 12 dragons on your gemstone island, 3 per island. As Shadur notes in the comments, you can also upgrade each section of the gemstone island for 25, then 50 gems, each upgrading allowing each "quarter" of the island to hold one more dragon. You can get 12 gems a week with a fully stocked, non-upgraded gemstone island, or up to 20 gems a week with a fully upgraded gemstone island. (Note it takes a whooping 300 gems to upgrade all island slots).
Note gems are mostly for extras; speeding up actions, upgrading certain buildings (the nursery) or buying special buildings (the extra breeding cave).
Ben Brocka's answer is certainly accurate, but I thought I'd do some dragon math for posterity, to share some of what I've learned about the game. Below is guidance to make coins as fast as possible (which can in turn fund treats for dragon leveling and decorations and other purchases for XP). If your goals are achievments, unique dragon collecting, park beauty, etc then of course take this guidance with a grain of salt. The spreadsheet I compiled to crunch all of this is epic in proportion, so if you've got some other nuanced question you want to know the answer to.. by all means ask.
Up through level 8, Small Fire habitats with 2 Flower Dragons are the most economical provided you check your park around 4 times a day (which you'll be wanting to do to breed, hatch, and feed). At level 8 you unlock the even more attractive Large Fire habitat, which becomes the best habitat (full with Flower Dragons) if you are checking your park more than twice a day. For below math I assumed checks are spaced evenly throughout the day, and dragon are level 6 (see more on that below).
| Habitat | Dragon | Checks/day | Coins |
|---|---|---|---|
| Small Fire | 2x Lv 6 Flower Dragons (2hr breed+incubate) | 4 | 30,000 |
| Small Earth | 1x Lv 6 Moss Dragon (24hr breed+incubate) | 4 | 31,680** |
| Large Plant | 4x Lv 6 Plant Dragons (30s breed+incubate) | 4 | 2,000 |
** considered disadvantaged due to breeding time and risk of breeding Tree Dragon (28 hrs lost)
| Habitat | Dragon | Checks/day | Coins |
|---|---|---|---|
| Large Fire | 4x Lv 6 Flower Dragons (2hr breed+incubate) | 3 | 45,000 |
| Small Earth | 1x Lv 6 Moss Dragon (24hr breed+incubate) | 3 | 30,000 |
At level 11-12 some options open up to you, and it becomes more about how you want to play the game. You can focus on some easily acquired dragons to start building a cash reserve, or instead start chasing the rares.
Some options to consider:
| Habitat | Dragon | Checks/day | Coins |
|---|---|---|---|
| Large Cold | 3x Lv 6 Lichen Dragons (12hr breed+incubate) | 3 | 112,320 |
| Large Earth | 3x Lv 6 Quake Dragons (12hr breed+incubate) | 3 | 159,840 |
| Large Cold | 3x Lv 6 BlueFire/FrostFire Dragons (24hr breed+incubate, rare) | 3 | 150,000** |
| Sun/Moon | 1x Lv 6 Sun/Moon Dragon (4 days breed+incubate, rare) | 3 | 233,280 |
| Rainbow | 1x Lv 6 Rainbow Dragon (4 days breed+incubate, rare) | 3 | 345,600 |
** Beat by a thin margin, but the best overall dragon/habitat combo above 3 checks/day through level 30.
Above level 12 the only really noteworthy unlock is the Large Metal Habitat. Once unlocked, and fully outfited with Magnetic Dragons it is the best non-rare 1 check per day habitat, at 115,200 / day.
The DragonVale Wiki has a great link on this here: http://dragonvale.wikia.com/wiki/Breeding_for_Profit
Assuming you keep your breeding cave fairly busy in the early levels, this becomes a more significant potential for revenue at higher levels. Consider:
Both of which are relatively easy to come by once you've unlocked them and have the cash for the eggs and habitat. If you really want to farm, some metal dragon hybrids have an even higher payout later (see the link).
Breeding is one of the main bottlenecks of the entire game, especially early on (unless you are buying trunks of gems with your real monies). As such, think twice about breeding mating pairs that have a potential for long cycle times. This is especially true of any earth combination, because even after such a long wait, what you get in return is typically not awe inspiring.
Best Answer
Yeah, just breed a Fire dragon with a Water dragon and you should get an Air dragon. I don't believe there's any other outcome for that breeding pair.