The game is simple. Build habitats and buildings until you reach your limit, based on your level. As your level increases you have access to more habitats and buildings.
At the start you will only be able to build Island Dragons and Earth Dragons. Later on you'll get a Crossbreeding building. For crossbreeding combinations, see Little Dragons/Crossbreeding.
You'll also get quests. To complete a quest, build the thing or hatch the dragon that it requires. A few quests require that you remove objects on an island, such as pine trees. After completing a quest you'll get a reward.
Starting out[edit]
At the start you'll want to focus on Island Dragons. They give coins at a high rate, but since they have a low coin cap, you'll have to monitor the game to get anything from them. This is where time investment, which could be considered a play style, comes in. If you don't want to, or can't, play much, invest in Earth Dragons, since they have a high coin cap.
You'll also need to watch your energy wells. In terms of efficiency, it is always best to go for the cheapest energy reward on the small wells. If you play for an hour you can get much more than it would have taken you to get the 300 energy for 24 hours of time. It will also be cheaper, and you'll be getting coins from your Island Dragons to make up for any you lose on the wells.
Second island[edit]
By the time you expand to the second island you'll have a big well or two. Since they don't have a short time duration for the cheapest level, always go for the 3000 energy reward. Math-wise, the cheapest Big Well reward is 300 Energy for 4950 coins after 2 hours. That's 3000 energy for 49500 (~25,000 coins cheaper than the highest reward) after 10 times, spread over 22 hours. You would have to be checking in on your game all the time, which could work if you're playing it on your phone. You'll also have to keep in mind when you won't be able to check your game (like when you're sleeping).
Around level 15, replace all of your little wells with Big Wells. At 16 you'll unlock the third well type, but imagine how much it must cost to use. Judge your income before investing in higher cost buildings.