Like other FTP (free to play) games, you can spend time to find what you need or you can buy (with real money) what you need and/or speed up certain processes (Expandning land, Upgrading your storage, building bridges/homes).
The amount of coins and crystals for homes, animals, etc. change as you go through the game, so if you see amounts listed on a website, know they may be different in your game.
If you want to buy crystals, the Bonus Pack that is over on the left side of your screen is a good deal - $0.99 for a Snowfall the White Tiger, 500 coins and 55 crystals (this could be different for you but will still likely be a good way to cheaply buy a bunch of crystals).
Try follow the quest line instead of wandering and doing random things to maximize the returns.
Try to log on back game if you can to collect coins and experience as often as you can. Once you have some homes for animals, they will generate coins after a certain amount of time (different for each animal home), so logging in at least once an hour is an easy way to pick up some coins.
Once you rescue an animal and bring it back home, you will need to build a home for it before you can send it off to an island. Before you can build a house (paid for with Coins), you have to Expand the land for that animal (paid for with Leaves). If you know you are going to rescue specific animal soon, Expand the land so that will have time to complete and will be ready by the time you bring back your animal. Once you have built a home for an animal, you can have more than one of that kind of animal live in that home, but you will have to pay to build the additional animals a room. Up to four animals can live at a home.
Keep farming fruit to feed your animals. Choose the fruit your most used animals need. Early in the game, that is blueberries. If you know you are going to rescue an animal that eats treats, use the Cookhouse to create the treats ahead of time to they are ready for when you want to use that animal.
Align crafting jobs in workshops and cooking jobs in the cookhouse for your up coming quest goals and bridges.
The Cookhouse is where you use fruit plus a flour sack to create blueberry, raspberry, and blackberry treats. Some animals will only eat treats, so plan ahead for which animals you want to use and make sure you have created enough treats for them using the Cookhouse.
Zoom out and move around your map to see all the available islands. Islands will move, appear and disappear. Even if an island doesn't have an animal to rescue on it, if it has an Anchor icon, you can still go there and clear obstacles to get to the crates. Crates can have tools, energy, coins, or even crystals. You can also sometimes get tools or crystals as a bonus for just clearning an obstacle, so whenever you visit an island, be sure to clear all of the obstacles.
Once your animal has a home, you can click on that home to play a Match 3 game. You will have to feed the animal in order to play the game. Each animal home has a different variation of the Match 3 game and some are easier than others. The more difficult the Match 3 game, the more coins and XP you get if you win, but you may not win everything you play the more difficult games/higher level animals. Play the Gorialla Match 3 game to get coins because it's easy and fast and a good way to raise money. The Gorialla eats blueberries, which is the fastest growing fruit, so you can you play the Gorilla Match 3 a lot. The Lynx Match 3 game is the second best Match 3 game (although you may not always win that one) and the Lynx eats raspberries.
Be careful how you use your crystals - they are the most rare. They can be found on islands (in glowing crates or as a pop-up when you clear obstacles), but it doesn't happen a lot. Otherwise you can buy crystals for real money.
When you get the Mystery Map, you get to open one door for free - if you touch any other doors, it will cost you 10 crystals, so be sure you want to use your crystals that way.
There are some animals who are on islands that can only be gotten to via bridges that cost crystals (such as the Stegosaurus). Some animals also have a time limit - if you do not get the animal before the timer on the map label runs out, that animal will disappear (for example, the Polar Bear).
You can "clear" an island by getting to all of the crates and Mystery Animals - you do not have to get rid of all of the obstacles (although you may miss out on some items that will pop-up if you clear the obstacles (flour, nails, spades, crystals, etc.). Since new islands will replace islands that are "cleared" this can be useful if you want a different island to show up.
You do not have to go to every island. Most islands now (as of mid May, 2014) have a timer. If the timer runs out, the island will disappear and (depending how many islands are already on the map), a new island will appear.