The argument is self explanatory. The universe, the earth, blah has been fine tuned fro life. Some take the argument further and say the universe, the earth, blah has been fine tuned for human life.

I'll start with the universe: The majority of the universe is empty space. The vast majority of the matter in the universe is in galaxy's with millions of light-years between them, the vast majority or all of the galaxy's are in large clusters with hundreds of millions to billions of light-years between them. Galaxy's them themselves are wispy things with most of the baryonic matter in nebula, stars and black holes.

Most of the "stuff" in the universe isn't baryonic matter (the matter we are made of). Most of the "stuff" in the universe is dark energy (about 73%) and dark matter (about 23%). Baryonic matter only make up about 4% of the matter and energy in the universe and most of that is interstellar and intergalactic gas (about 0.4%).[1][2]
Then there is space itself. Beyond the protection of the earths magnetic field you have cosmic rays coming at you from all directions, coming from stars, gamma ray bursts and the sun. Cosmic rays can damage DNA.[3] If your hit by a solar flare, your dead.
Space is cold, very cold too cold for life. Beyond the inner solar system the only places that could have life are are moons of gas giants large enough to have an atmosphere and close enough to the planet so that the gravitational title forces to heat the moon enough to have a liquid ocean. And too close to the sun its too hot for life.
As for other stellar systems: We don't know how common planets are, we have found other planets but nothing earth like because we are unable to find planets the size of earth, we can only find planets that are large enough for their gravity to cause their star to wobble so we don't know how many earth like planets are out there. However we do know from our own solar system that planet formation is quite chaotic. Venus rotates very slowly in the opposite direction from the rest of the planets in the solar system, Uranus is on its side and the earth is the only planet with a single large moon. The best explanations for these are planetary collisions.[4][5]

Sometimes used with the "universe is fine tuned" argument or could be used as a rebuttal to the points above: the claim that the Earth is fine tuned for life. Of course it isn't.
The best they have is "the earth is in the perfect place for life to exist. A little bit too close and the earth would be too hot a little bit to far and the earth would be too cold." But that claim ignores one huge fact, the earths orbit is elliptical, the earth does get closer and further from the sun. Further more the habitable zone of the Sun is estimated to be between .95 and 1.37 AU (and AU is the average distance between the earth and Sun) so the Earths orbit is not fine tuned.[6]
While it can seem that the earth is fine tuned to life or even us, its not. Life is very adaptable, there are animals living deep in the ocean, animals can live on mountains at reliantly high altitudes there are even worms living in glacial ice.[7] Live is very adaptable. The earth is not adapted to life, life is adapted to it.
Life on earth lives on a thin layer of crust, the vast majority of the earth is uninhabitable. It's far too hat in the mantle, its far too hot in the core, it is only the crust where life can live.[8]

Now to the idea that the universe is fine tuned for human life: We only live on 1/3^rd of one planet. We can't live in the oceans, we can't live in space. And much of that land is difficult to survive on. We have thin skin, we cool our selves through sweat, we lack the fur and body fat needed to protect us from the cold. It is our large brains and opposable thumbs that have allowed us to survive. It is our intelligence that allows us to survive in the desert, we had to learn how to survive in the desert despite our cooling system that causes humans to loose water much faster than other animals. We had to kill other animals to get they're skin and fur to protect us from the cold of colder environments. It is the development of farming that made us the dominant species.
Its not that the earth is fine tuned to us it's that we have the intelligence to learn how to survive and are adaptable enough to survive. But we are not the most adaptable things on this planet. Smaller simpler organisms are far more adaptable than we are. Single celled organisms can adapts and thrive in environment that are very hostile to us. [9]
If the universe is fine tuned for life, its not fine tuned for us.

Then there is their best argument: "If gravity was a tiny bit stronger or weaker or if the electromagnetic interaction was a little bit stronger or weaker blah, blah, blah"
This argument has two problems. The first one is that the assumption that if the the strength of the fundamental interactions were different life could not form, that assumption is baseless. If you change them enough then yes, stars would never form, etc but the claim that changing them slightly makes life impossible is baseless, there is no evidence to support it. Second: Fred Adams of the University of Michigan Ann Arbor tested the assumption using a computer simulation. He found that if the fine-structure (alpha) and gravitational were off by as much as a hundred fold stars would still form.[10] In fact it is conceivable that if the strength of the fundamental interactions were different life may be more probable.
© 2009 all rights reserved

Sources
1. Imagine the Universe - Dark Matter
2. NASA Home- News and Topics - Universe
3. Wise Geek - What are the Health Effects of Cosmic Rays on the Human Body?
4. Ask an Astrophysicist - Retrograde rotation of Venus
5. Universe Today - Formation of the Moon
6. Stars and Habitable Planets
7. Ice Worms and Their Habitats on North Cascade Glaciers
8. Structure of the Earth
9. Eukaryotes in extreme environments
10. New Scientist - Is our universe fine-tuned for life?

<-Part 2 | Part 4->