A debris hut is like the pile but with an infrastructure. Similar to a lean-to except closer to the ground and built to your body's proportions, a debris hut can last months with minimal maintenance. In the woods you'll build it with sticks and leaves, in the city you'll use whatever non-toxic materials are on hand. It doesn't really matter how good your shelter looks though, just as long as it has the dead air space you need to keep warm (leave the fashion statements and lavish mansions for the vampires trying to suck your blood).
You'll need to filter and boil your water to make it safe. Most of today's water is contaminated with biological contaminants like Giardia spores, which will make you crap your pants until the sun don't shine, so you'll need to boil your water to destroy them. Also, just to make water safer in general, bury your own feces above the waterline (you can tell where this is by the sudden shift in leaves, sticks, etc.). For an easy filter, take a sock, add charcoal, sand, then grass. This'll remove dirt and debris along with some chemicals (filter until it's clear).
That covers flowing water, but there are other sources that are already safe. Dew, whether you collect it with a cloth to squeeze into your mouth or lick it off of grass like in The Gods Must Be Crazy, is always clean. You can also drill a hole into the largest side of a Sycamore for water (only one per tree and tap the hole when done), peel then chew up Thistle, or build a solar still using a sheet of plastic, a tube, a cup, two rocks, and a hole in the ground. All of these'll give you clean, fresh water that won't leave you running for the bushes.
Not having enough water can be horrible, but having none is far worse. The longest I've gone without water was two days, and by the time I drank again I felt like I would die. (Never do this. It was stupid and you should learn from my mistake.) My skin grew clammier until it seemed like clay, and I got a headache that escalated until I was staggering in pain. The psychological effects were the worst though - I started wanting to really hurt myself, and felt like I could drain my veins just to feel dampness on my skin. At this point, I decided I'd learned enough and started drinking again (I prefer my near death experiences to be from driving on the highway, thank you very much).
Everyone experiences dehydration differently though, so your main indicator should be the one everyone shares - pee. Your urine should be clear: Any yellow is a sign of chronic dehydration (I believe the first sign of over-hydration is known as drowning).
Finally to food, the most consuming of all needs. As the last man on Earth, you're stuck with hunting and gathering for sustenance. In a Zombie Apocalypse there should still be plenty of plants and animals left since the formerly-deceased aren't interested in plants and animals are too fast and stealthy for shambling corpses. Plants and animals should also be around in the others (if they weren't then the earth would have run out of oxygen), so you'll need to go where they'd be, and water is as good a place as any to start looking.
People instinctively walk towards water so don't worry about finding it (try downhill if nothing's working), and check the trees. Acorns are edible after a few boilings (or just eat them straight if you don't mind the non-poisonous but overpoweringly bitter tannic acid), and you can grind up the inner-bark of Oak trees to make flour. Grass is edible, as are clovers and their flowers; pine needles are good for tea, and the nuts from pinecones are edible.