This guide was written and first published by Vovin on the Touch Arcade forum. Thanks to him for giving us permission to post it here.
The first day or two should mostly be devoted to gather supplies and doing "chores". Just keep in mind that the game gets really intriguing once you get into it, and above all have PATIENCE.
1. After the tutorial, your first way goes straight up to the house on the hill. Loot the three chests, you might find medicine, bandages, a radiation suit, food, clothing (leather pants) and a lot of other useful stuff. Meanwhile, three wolves should have appeared at the house. Wait for them to come up the first set of stairs, the usually won't climb the second set. Stay up there until a wolf approaches, and when he turns around to go away a short distance, run down, hit him with your axe and back up the the second level of the house. Repeat until all three wolves are dead. If one runs away, chase and kill it. This process shouldn't take more than 2-3 minutes. Now you can use medicine or bandages if you are (still) bleeding.
2. Go down to the small house at the beach and check out the chest. Go outside and cut down some trees for wood. Build a second chest and put it next to the first in the small house. It's a very safe location, cause animals won't enter there normally. Also make a backpack to carry around more stuff (if you need more leather, just kill 1-2 more wolves).
3. Go to the old facility, inside are 6 chests, and at the farm behind the facility, another 5 or 6 chests are waiting for you. Loot everything and carry the stuff back to your small hut. You should have quite some materials and some food by now, as well as a bow and arrows.
4. Grinding time! Now, after getting all the stuff from the 10-12 chests, spend rest rest of the entire day to run over the beach, collect bananas, pineapples, coconuts, twigs, stones, flintstones, pebbles and all stuff lying around like crazy. You need that stuff later, no kidding.
5. Make a few more axes and pickaxes and mine the stones on the beach for materials, also chop down more trees to collect wood. From time to time, unload the stuff into your chests. If wolves approach, no prob because you should have a bow, some arrows or even a gun/rifle by now.
6. Get used to always have an eye in the upper left corner on the focus symbol. If it changes into a claw, danger is near. Just tap it to see where the bad guys are located, your camera will focus automatically.
7. By the end of the day, your should have a big amount of fruits, fish and/or meat as well as stuff to craft things. Make a nice fire on the front lawn and have a good night.
8. Before going to sleep, you can also try to make more clothing when the night falls, or make other useful stuff you need. PROTECTION is really everything. But because of the work you've done, you're now able to concentrate more on the gameplay in the next days, with all those ressources in your chests you'll be fine for now and you can start to explore.
9. A last advice: don't make yourself a home at the beach.Try soon to find an unoccupied building in or near the center of the first island to set up your first bigger base. If you don't want to run several miles each time. Unless you don't care.
10. Have fun and don't let your brain get eaten.