Let's say you survive your ship sinking or plane crashing and wash up on a beach of some small uninhabited island (but clearly visible vegetation) with supplies roughly the equivalent of a good commercial 3-5 day survival kit. You know roughly where you were when you had your mishap but now you could be a long way from where it happened and you don't know when or if you'll be rescued. What would you do to survive and be rescued?

Firstly, sit down, make a cup of tea and think.

Inventory supplies and skills available.
Read and follow survival kit instructions.

Probably have another cup of tea.

Whether good or bad, I would spend a lot of energy hiking around. It would take me awhile to believe I landed on an island where humans are neither living nor exploring. After coming to grips with that reality, I would freak out for at least a moment. Then, I'd concentrate on breathing in-and-out for awhile and doing nothing else, until I calmed down. Then, I would do what I've been trained to do and what my intelligence would allow me to improvise.

First, scene safety. If there are any IMMEDIATE threats (wounds that need treating, potentially injurious situations), deal with them.

After that, Stop, Think, Observe, and Plan.

If there's a working communication device (PLB, SEND, cellphone with signal, radio) it's time to start signalling for help.

Staying put or moving is going to be a decision based on shelter, water (and possibly food) availability, my physical condition, the clothing and particularly footwear available, tools and the rest. If I'm uninjured, wearing clothing and footwear appropriate for the environment, there are no resources nearby, and immediately find signs of human habitation, I'm almost certainly going to attempt to self-rescue.

If I'm hurt (particularly in the legs or feet), barefoot, need to build shelter immediately to survive, there are lots of resources nearby, and see no signs of human habitation, I'm almost certainly going to stay put and do what I can to make myself visible and safe.

In an in-between situation my inclination would be towards building a reasonably-sustainable shelter, collect resources, and consider moving to terrain that gives me a better view of the surrounding area and see if self-rescue could be a viable option.

Wow, a whole island, if only...

I thought about this a bit before equipping my aviation survival vest. In the various pockets were an ACR ResQLink PLB, a GPS and a marine VHF radio, among other things that would be good to have on a life-raft (or just floating without a raft) at sea.

To the question at hand: After an initial call-out on VHF Channel 16, failing to get a response on the radio, I'd activate the PLB and then build a nice signal fire.

In a situation like this your ability to signal for rescue is really important. With a PLB, you only need to survive until rescue arrives. With a PLB that might be a few days in a really remote area; without a PLB it might be a few (or more) years. Ask Chuck Noland if he'd rather have a PLB or a basketball while marooned...

I think I would stay quiet and enjoy the peace for a while before I signaled anyone.

I agree with Montenaro!!!!

That's funny When I thought about this scenario, certain films like Cast Away, Black Stallion and even Lord of the Flies came to mind...

In all seriousness though, you would follow the proper priorities (first aid and safety, shelter, water, signal, fire) and then take stock of your environment. Find what resources are available and what the possibility of rescue is (proximity to population, sea or air routes). If it looks like rescue may be far off, start setting up your living quarters, gathering resources and make your signaling devices, like a very large SOS that could be seen from the air.

After that it is waiting and trying to maintain a positive attitude. Get comfortable, try to sleep well and keep yourself occupied improving your situation.

If you can make a hammock and pina coladas from the coconuts, all the better.

If your flying commercial you are probably, as they say, deep in it. So let's assume your in a light plane and a have few options. I really hope there is fresh water. Otherwise it's just become academic.

So, get my signals set up, Shelter organised etc. Start fishing for my supper. That means hook and line along with every fish trap that my ingenious (and highly motivated) little mind can improvise.