More than you might think.
Broadly, effects of a nuclear blast fall into two categories: electromagnetic radiation, and kinetic blast.
In the first category, we have:
1. Nuclear radiation.
This is the gamma rays, neutrons, and other ionizing radiation resulting directly from the nuclear fission and fusion going on at the heart of the bomb. Some of this stuff travels at the speed of light, so it will be the first thing that hits you. If you are at a great enough distance, it will merely give you cancer, from which you may die some months or years down the road. At distances closer than that, it will disrupt your body's electrochemical systems (i.e. your brain) and kill you instantly. Nice.
2. Infrared radiation.
Otherwise known as radiant heat. Also being electromagnetic in nature, this reaches you with the visible flash. At great enough distances, you may simply feel the warmth; as distances decrease, you will experience first, second, or third degree burns. (A third degree burn is defined as "charring".) As more of this radiation continues to pump into you, you will be incinerated. At very close distances, you will simply be vaporized -- more or less instantly.
The other category includes effects which are propagated by the atmosphere, as opposed to radiation, which needs no medium and can travel quite easy through empty space.
When a nuclear bomb detonates, it creates a fireball of rapidly expanding plasma and gas. The pressure within the volume of the fireball is enormous -- almost not worth contemplating. But outside the fireball, a pressure wave expands outward very rapidly, well in excess of the speed of sound. At any given instant, the atmosphere outside this radius is "normal", and the atmosphere inside this radius -- the zone of the blast's effect -- is very high pressure and very hot.
If you survived the radiation emanating from the bomb, then you have to contend with the following effects:
1. High pressure.
The "over-pressure" within the radius of the wavefront can be enormous, depending on the distance. Once the fireball has stopped expanding, the pressure within the radius diminishes with the volume -- that is, as the cube of the radius. But consider that humans cannot survive overpressures of more than a few pounds per square inch. You will be "crushed" by the pressure. At the very least, you will not have the strength to take a breath against that pressure.
2. High wind.
The wavefront travels outward from the center of the blast faster than the speed of sound. Behind that wavefront, the atmosphere is following at a very high speed (again, depending on the radius and the time since detonation). Wind speeds of over 200 mph are typical. A wind speed of 50 mph is sufficient to knock you down and slam you into whatever obstacles are nearby. A wind speed of 80 mph is more than enough to drive loose debris through your body. Winds over 100 mph are very hard to survive. Assume that a wind speed of 200 mph is going to be fatal, in some way or other.
3. Heat.
The atmosphere behind the wavefront has been heated by the nuclear blast. Temperatures well over 120 degrees are typical (again, depending on the distance and the time since detonation). If you do manage to suck in one breath, your lungs will be cooked. Otherwise, you are baked.
Given the above considerations, arranging your survival through a nuclear detonation is a difficult endeavor.
And then, if you succeed at that, you'll have to contend with the longer-term effects of the blast. Besides the obvious destruction of habitat, these effects have to do with lingering radiation, which are of two main forms:
1. Nuclear fallout.
The fireball rises very rapidly into the atmosphere, and typically evolves into a vortex, i.e. a "smoke ring". The convective action of this process is strong enough to draw quite a bit of soil and other surface material into the air. This material is vaporized and, through intense bombardment of nuclear radiation, made radioactive. Eventually this material condenses again into dust particles of the elements or simple compounds: iron, silicon dioxide (sand), and so on. These particles precipitate onto the ground at some distance downwind of the detonation, covering you and your environment in radioactive material. Worst of all, these dust particles get inhaled, subjecting your lungs and internal organs to ionizing radiation at very close distances. This is cancer city.
2. Direct radioactive conversion.
The intense nuclear radiation from the bomb blast directly converts matter, within a certain radius, into radioactive isotopes. Thus, some circular area centered on the blast will be an uninhabitable "hot" zone. But unless you have some kind of radiac, you won't know; these radioactive emissions are completely undetectable to human senses. If you so much as walk through this zone, you will be looking at lethal cancers in the not too distant future. It could even kill you outright.
I have not addressed other potential post-apocalyptic sources of death, such as zombies, day-glo-mohawked gasoline freaks, or trigger-happy survivalist bunker-dwellers.
Have a nice day.
