You can get more Dragon Gems in a few ways.
1. Shop for Dragon Gems
There is a Dragon Gems shop that has many options, including 30 Day Dragon Gem Payout, special 1 time only Bonus Gem packs, and a range of other bundles. (The 30 Day Magic Gem Payout is a great place to start.)
Open the shop with this button:
2. Complete Quests to find Purple Dragon Stars
If you want to find Gems while playing, the main way to get them is by finding purple Dragon Stars, then tapping them for Gems. However, if you know these tips, you will be able to save up a lot more:
  • Play Quests!  Every time you complete a quest, there is a small chance that instead of a normal, yellow Fallen Star, a purple Dragon Star will appear. This is completely random -- there is no tally or anything that causes more or less at any point. It is entirely based on luck! So you can expect some streaks where you don't see one for a long time, and then others where you get more.
  • Bring them to Camp!  If they appear in a level, don't tap them! Instead, leave them there, and when you win the level, they will show up in the reward menu to bring back to camp for free! Why do this? So you can save them up and merge them!
  • Merge them in 5s!  When you have saved up *5* purple Dragon Stars, merge them all at once. Don't merge 3 (it's less efficient). There are 2 levels of Dragon Stars, so once you merge them, you can tap them for gems.
  • Merge the Gems in 5s! There are 3 levels of Gems, worth 1, 5, and 15 Gems. Merge level 1 and 2 Gems in sets of 5 to get the most results! Then collect any level 3 Gems.
It takes some time to save up purple Dragon Stars and Gems to be able to merge them, but it is worth the wait!
3. Find Gems on Land
The last way to find Gems is that sometimes they or the purple Dragon Stars are on the dead land in Camp. But these are rare.
You can also unlock the Premium Land under the Gold Clouds to find a bunch of Gems and purple Dragon Stars (among other things, like eggs and nests, etc). You will need the right amount of Dragon Power first, and then you will have the opportunity to purchase the land.