To make a basic shelter, I'll need sturdy branches, some leaves, and plenty of vines. The leaves will act as a roof to keep out sunlight and rain. The branches will be used to elevate and support the roof. The vines' purpose is to tie the two together to keep it from falling down on me. With a place to rest and keep out of the shade, I would only have to worry about making fire.
Fire is as simple as it gets. I have wood and I have vines. All I need to do is create enough friction on the wood using the vines to start a fire. Hopefully, by making a huge bonfire, I can alert far away ships of my location so that I can get saved. However, if I consider that nobody will come save me, I'll need a way to entertain myself and make life easier on this island.
To that end, I will need to make tools. Tools will enable me to partake in larger scale projects such as gathering different kinds of food, create larger structures, and protect myself against predators. Using stones, vines, and wood, I'll be able to create axes, knives, and spears. With this, I can go spear fishing in the water, chop down trees to make a better shelter, and hunt birds for food and feathers (to make arrows to use with a bow).
As you can see, fruit bearing trees and a source of vines and fresh water would not only enable me to survive on a deserted island but comfortably live on it.