What happens to the person is simple. What happens to their body involves a few more steps.
The first thing that happens is you scream. Well, you act to scream or the scream acts on you. The lungs are designed to withstand about 1/10th of an atmosphere of pressure, which is the typical delta occurring during breathing. You either scream all your air out of your lungs, or that air forces its way out, doing substantial damage along the way. This effect is probably not all that important for someone being executed by vacuum. For those who want to live, it matters greatly. Divers engaging in what is called a Controlled Emergency Swimming Ascent (CESA) learn to exhale while they are ascending to give the air in their lungs a way out. This decidedly unintuitive maneuver is essential for your survival.
The next thing happens is that you lose consciousness at around 15 seconds. The lungs are a powerful gas exchange mechanism, and you just exposed them to pure vacuum. The vacuum rips the oxygen right off of the hemoglobin, and then delivers that blood to the brain. 15 seconds later it reaches the brain, and you lose consciousness almost immediately after that. Death arrives soon after, as if the heart stopped beating (it may be beating, but it's not delivering oxygenated blood, so it's not helping at all).
You can survive like this for a while:
... one 1965 study by researchers at the Brooks Air Force Base in Texas showed that dogs exposed to near vacuum—one three-hundred-eightieth of atmospheric pressure at sea level—for up to 90 seconds always survived.
After that, the answer is a bit more boring. You do have issues with water boiling, but its not instantanious. Space is actually a very poor conductor, so it doesn't conduct any heat away. Your body radiates at a very low rate. Almost all of the cooling comes from evaporation, which is a very localized effect. Astronauts involved in accidents like this remember feeling the evaporation off of their tongue before losing conciousness. However, this takes a long time. At least as long as it takes to freeze in a cold weather environment. The cool needs time to work its way in (or, phrased the other way, the heat needs time to work its way out). Your eyes, however, do not typically "explode:"
Water in the soft tissues of your body vaporizes, causing gross swelling, though the tight seal of your skin would prevent you from actually bursting apart. Your eyes, likewise, would refrain from exploding, but continued escape of gas and water vapor leads to rapid cooling of the mouth and airways.
In fact, one of the new space suit designs, the Biosuit actually takes advantage of this. Human skin can actually hold its own against a vacuum on small scales. Obviously, large areas of skin suffer from expansion due to fluids entering the area, but if you compress the skin at a gross level, the microscopic structure can take the vacuum. The biosuit is actually not vacuum tight. The air can escape through the weave of the suit. The result? Your body can actually cool itself via presperation just like it does in the hot desert sun! Your body emits sweat like it usually does, and that sweat evaporates into the vacuum, cooling you off!
Not that that makes me any less disturbed at the idea of exposing my skin to the vacuum of space, but it has been done. One of the more famous leaks on the ISS was resolved by covering it up with a thumb. (the hole was obviously later fixed more permanently, first by Kapton tape, and later I believe it was cemented shut)
Once the effects of evaporation stop mattering and you become inert, what happens to the body is exactly what happens to an asteroid of similar size. If its in an environment that gets hot due to the sun, it gets hot. If it's in an environment that gets cold, it gets cold. This happens on a long timescale, at least compared to the 15 seconds of meaningful screaming.