The initial challenge is figuring out what is really important and then focusing. While this is going on, it is nice to provide the organization with some framework within which to work. Setting the framework is a decision, or action, that has low risk, immediately communicates to employees, and makes the organization turn to your way of managing. This is particularly important if you are following a manager who had a style much different from yours.
The internal climate
What I did early on was important for the future because it started the process of making the company more customer focused. Prior to my arrival, the company had earned a reputation for being difficult to deal with. Our early actions made it clear that we intended to change and set the tone for the coming years. Similarly, the way I dealt with people within the company early on established the internal climate of the company from that point forward.
Flexible management style
A GM must proactively manage the corporate atmosphere, and this requires one to adjust her/his management style as the situation (current or future) demands. However, this can present an interesting problem in dealing with your associates (peers and subordinates).
General management seems to be a synonym for "trade-offs." Often what you want to do to improve one situation can hurt another situation (e.g., accelerated delivery helps sales and hurts development and customer support). As such, much of the data you gather can appear to be conflicting. Therefore, you have to be able to analyze the data, decide what your priorities are, and act against those priorities. To do otherwise can lead to inconsistency, a big morale and leadership killer.
Simplify. The more you can distill strategy and tactics to a few key points or priorities, the more likely the organization can respond. That's not to say your strategy should be simple; rather, it needs to be distilled to a few key directions or action items for each of the parts of the organization that need to respond.