It is worth beginning by stating that Kant believed very strongly in original sin, specifically in the corruption of every human nature. (He does not believe in original guilt, nor does he believe that this corruption is inherited - rather it is chosen in some way by the individual). He sees the evidence of original sin, which he defines as the adoption of a bad moral principle, in human behaviour. People act badly, therefore they must have chosen to pursue bad ends.
Despite this, human beings have a duty to be moral, indeed, perfectly virtuous. This is our moral end. (Incidentally, you cannot really argue for this; on Kant's view it is simply the case that we have a duty to be perfectly virtuous). As well as a moral end, human beings have a natural end, which is perfect happiness. Although the moral end and natural end belong together, and together constitute the highest good for human beings, Kant is clear that the moral end is more important than the natural end - it is better to be virtuous than happy. But the most important thing is that we cannot have a duty to be happy, whilst we do have a duty to be virtuous.
From this, Kant derives the concept of God, in three distinct ways:
1. I cannot have a duty to do what is impossible for me; moral perfection is impossible for me in this life; nevertheless, moral perfection is my duty; therefore there must be an afterlife in which I can continue my progress. (Thus the immortality of the soul is proved - not yet God, but God is very much connected with the concept of the soul).
2. The moral end and natural end of human beings belong together, viz. the good deserve to be happy; but it is often the case that the good are not happy and that the causal link between virtue and happiness is obscured; nevertheless, it is our duty to pursue a situation where the highest good (i.e. the correlation of virtue and happiness) obtains; this situation can only obtain if there is a just, omniscient, omnipotent God.
3. It is my duty to be morally perfect; but in fact I have an evil disposition due to my original choice of an evil principle; therefore, even in eternity I could only ever make progress - I could never actually be perfect; but I cannot have an impossible duty; therefore, there must be a God to make up the shortfall.
I have perhaps not stated those arguments in their most clear and impressive form. It isn't that important. The most important thing is that for Kant God is a concept to make morality work. In fact, in Religion within the bounds of mere reason, Kant is clear that an actual God may not be necessary - it is only necessary to recognise that the idea of God is possible. If God is possible, then there is hope of our duties being possible, and so we will not despair of them. God is a "practically necessary hypothesis", a "postulate of practical reason" - nothing more.
The grand weakness in all Kant's argument is simply put: Nietzsche. Even assuming the validity of Kant's arguments (and that is assuming a lot), there is still the fact that we must assume the duty to be moral. The arguments boil down to: morality only works with God; morality must work; therefore God. Nietzsche will categorically deny the minor premise - and where is God then for Kant?
I raise this because arguments like this are used regularly by Christian apologists - I have used them myself in the past. They are weak, extraordinarily weak. They may have had some subjective appeal in an age when people believed in objective morality, but I think the time has come to drop them. We can still point out that ethics only makes sense on Christian presuppositions, and this may be useful in getting others to re-examine their worldviews, but we need to understand that this in no way proves God, or even contributes a gram of evidence for his existence.