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His argument is fairly simple. First, either God exists, or God does not exist - there are obviously no other options. Secondly, a person can either believe God exists (and supposedly thus act in accordance with the Bible), or not believe God exists. Thus, there are only four possible scenarios combining all these possibilities.
1. God exists, person believes. In this case, according to Pascal's Christian definition of God (from the Bible), the person goes to Heaven, a reward or gain which is infinite.
2. God exists, person does not believe. In this case, the person goes to Hell, a punishment and loss which is infinite.
3. God does not exist, person believes. In this case, Pascal claims that the person will still benefit (by a finite amount) by being a virtuous and moral person. Now, most non-believers are quick to point out that one needn't have religion to be virtuous and moral; however, the argument will supposedly still work out the same if the results of belief when God doesn't exist were that you wasted the only life you had and the brain you possessed (finite loss).
4. God does not exist, person doesn't believe. In this case, Pascal thinks the person will be immoral and thus unhappy. And again the argument supposedly still works, even if we don't accept that but instead consider that the person would gain a happier life, with more freedom of thought and life without the crutch of religion (finite gain).
From this, Pascal uses common sense in concluding that the obvious best choice is to believe - since that way you have a possibility (however small) of infinite reward, and perhaps more importantly, you avoid the possibility of infinite punishment altogether. No matter how small the chance of God existing, or how big the loss for belief or gain for non-belief, the infinities in the first two options would always be the best bet (a gambler always goes for the best ratio of risk to reward and both the infinite reward of Heaven and infinite risk of Hell override any finite factors). As to the fact that his argument hinges on the ability of humans to choose what they believe, he says that even if you can't choose to change your beliefs, you will do so automatically by choosing actions that immerse yourself with believers (attending church, reading the Bible, etc.).
The argument seems convincing at first, but with more careful consideration its flaws quickly stand out. His argument deals entirely with the God of Christianity, and the Heaven/Hell that religion offers. However, other religions contain similar infinite rewards and/or punishments for certain beliefs or actions; and those religions are almost always mutually exclusive with Christianity. So choosing to believe in God may assure you of avoiding Christian Hell and even offer a possibility (however small) of Heaven, but it also automatically assures you of eternal punishment in countless other religions if they turn out to be true and Christianity false. A counter example helps illuminate this objection to Pascal's Wager.
Imagine one day you meet a man on the street, and he claims that he has amazing, limitless powers. He informs you that if you don't give him all your money, possessions, labor and worship, becoming a slave to him for life, he will damn you to infinite and eternal torture in a fiery abyss of pain. If you do what he says, he claims he will reward you with infinite and eternal happiness. Now, obviously what he says is either true or it is false; and you can choose to either grant his request or not grant it; these are the only choices. If it's true and you grant his request, you gain infinitely. If it's true and you don't grant his request, you lose infinitely. If it's false and you grant his request, you've wasted your life and possessions (finite loss). If it's false and you don't grant his request, no big deal. His friend who was standing there listening to the whole conversation tries to help you make up your mind. He points out that since there is an infinite reward (and punishment) associated with the possibility of it being true, but only a finite gain or loss associated with it being false, the reasonable thing is to grant the request. So would you hand over your money, possessions and indeed very freedom to this man you just met a minute ago? I think not (if you would, please mail me your life savings for which I will give you infinite happiness; otherwise I will use my limitless powers to condemn you to infinite pain).
So even if you accept Pascal's basic argument, it is obvious that it is rendered meaningless by the fact that multiple (indeed, perhaps infinite) mutually exclusive scenarios with infinite reward and/or punishment are put forth. A reasonable person in any situation like this certainly should not bet on one of the many possibilities (which leaves him open to countless possibilities of infinite loss, and of course a guarantee of finite loss in this life), but withhold any bets and enjoy that which is known for sure and requires no such bets - this life.