If you're having trouble surviving, combine cloth and alcohol to make molotovs. If you manage to hit a cannibal with it, it's a one-hit kill (after a while, anyway). If you get captured, don't leave the cave you wake up in without the flare gun; it's also a one-hit kill weapon.
As others suggest, when you start, grab what you can carry from the crash site but do not spend very long there. Supposedly taking the axe from the woman's stomach triggers a cannibal scouting party, but on my very first playthrough, I clipped through the side of the plane and fell out, staring right at a cannibal leader who was staring right back at me BEFORE I took the axe (I was crouching the whole time, so I can confirm that they can see you even while you crouch), so even if you leave the axe, they can still come. If you make it away from the crash site without being seen, try to get out of the forest. Being away from the trees makes it harder for cannibals to sneak up on you. When choosing a site to build, stay away from the forest, the big gnarled trees, and the effigies and try to pick a spot that has natural shelter from several sides, like in between large rocks. The key here is that while you don't want cannibals to find you, you REALLY don't want them to find your shelter, because once they do, they'll start occasionally returning to that spot to look for you and see if you're home. Along those lines, if they spot you out and about, don't run back to your shelter; run somewhere else (or fight). Wherever you build your shelter, if you want to stay hidden, do NOT light a fire near your shelter. Having a fire going might be comforting and the survival guide says it will frighten predators, but it will attract cannibals at night (when they're particularly aggressive). Along those same lines, don't go wandering around at night. Try to sleep in your shelter through the night. If you wake up before dawn, it means there are cannibals nearby, but it doesn't necessarily mean that they have found you. Stay crouched and try to remain hidden.
On the flipside, if you're more the fight type than the flight type, if you kill all the cannibals who come anywhere near your shelter, you might be safe for a while. Once I got the flare gun, I killed two or three scouting parties with it, and didn't see another cannibal again (I quit that game 3-4 in-game days later), though I stayed near my shelter and only went as far into the forest as I needed to in order to gather logs and sticks.