On February 5, 2010 President of Russia formally approved the new military doctrine, whose text is now available, and a document called "Basic principles of state's policy in the area of nuclear deterrence through 2020", which appears to be classified.
Nikolay Sokov, who has been following the Russian doctrinal debate closely, has a detailed analysis. The key point, however, is that despite the earlier signs that the doctrine would expand the use of nuclear weapons and even allow for preventive and preemptive strikes, the final document is quite reasonable. As far as nuclear weapons are concerned, the key statement of the new doctrine is that
Russia reserves the right to use nuclear weapons in response to a use of nuclear or other weapons of mass destruction against her and (or) her allies, and in a case of an aggression against her with conventional weapons that would put in danger the very existence of the state.
This is, actually, not bad, since the scope of the use of nuclear weapons is quite limited. For example, a limited conventional aggression against Russia would not trigger a nuclear response. Neither would a "regime change" in an allied country, as long as it doesn't cross the nuclear threshold.
Of course, it is a declaratory policy and one can argue that things may change in a heat of a crisis. This is true, but the doctrine sets a baseline, which says that Russia is quite restrained in setting goals for its nuclear forces.