A one-paragraph explanation of the Austrian theory of business cycles would run as follows. Interest rates are held at too low a level, creating a credit boom. Low financing costs persuade entrepreneurs to fund too many projects. Capital is misallocated into wasteful areas. When the bust comes the economy is stuck with the burden of excess capacity, which then takes years to clear up.
This is reasonably accurate. Unfortunately, this explanation is not terribly unique to the Austrian school. The Keynesian school proposed that there could be a credit boom (although they were less apt to blame the government for the fact that interest rates were too low). In fact, in a bit more precise way of looking at it, uncertainty and adaptive expectations (what Mr. Keynes called "animal spirits") play a more prominent role in the boom and bust cycle in the Keynesian model. It turns out that this is also true of the Austrian school. In fact, both schools attribute some of the fluctuation in the business cycle to a "coordination problem" in the processing of information revealed by noisy market signals.
OK, so where are they different? Well, basically on the matter of policy response. There is some evidence that keynesian deficit spending can help. There is other evidence that shows that a more austere approach is better. As in all things it is probably simply the case that the devil is in the details. Government spending is probably most helpful when it is invested in things that would be useful to have anyway (like roads, bridges, and energy infrastructure), and not simply money transfers that just substitute for other spending now or in the future (like transfers to states, tax cuts, or entitlement spending).