The title states it all.
The cloud of gas and dust the solar system formed from was not perfectly stationary, but had a net angular momentum. This initial angular momentum eventually led to just about everything about the solar system rotating/orbiting in the same direction.
Why did it start spinning?
Angular momentum is a conserved quantity.
This question has been asked many times; a quick google search will reveal this answer at Cornell University's "Ask an Astronomer" pages: http://curious.astro.cornell.edu/question.php?number=416 [Broken]
It will also reveal this question has been covered here more than once. For example, see [thread=146220]this thread[/thread].
What is the origin of angular momentum in the universe?
Angular momentum is a property of objects like mass. An object can have one of an infinite number of possible angular momentums, but zero is only one of those numbers. So the odds of finding a complex system with zero angular momentum are extremely small.
How can an object have an infinite number of possible angular momentum values? I thought that every particle had a set spin(+/-) that it has to have, or am I misunderstanding what you're saying? If you look at the universe as a whole, is its angular momentum 0?
An object only has one of a possible infinite number of angular momentum values. What the actual value is is essentially random, just like the mass of a random cloud of gas and dust is essentially random.
So you're saying that an object's angular momentum is dependent on its constitutes? Is it the combination of the spin of all of the particles that compose the object? If so, how does an object start spinning? I can start spinning in circles right now without altering my composition(at least to a significant degree.)
I strongly suggest you do a tiny bit of research of your own on this topic. Google the phrase "why do planets rotate on their axes". Read up on the subject, then ask questions. The reason you have been getting curt answers is because the answer to your question is freely available on the web. If you still have questions after doing just the tiniest bit of work on your own we will be glad to help.
This has nothing to do with the quantum mechanics phenomena of "spin".
If a group of objects are moving relative to each other in any direction other than along a line through them (ie, if they have any tangential component of velocity), they have an angular momentum.
I've been giving short answers because there really isn't much to say about the issue!
It sounds like the OP is stuck on the "first cause" of angular momentum.
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