Under the terms of the Palestinian constitution, President Mahmoud Abbas is likely to ask Hamas to form a new government. Hamas will likely make a public offer of a coalition to Fatah, but right now it's unlikely that Fatah will join them. There is widespread opposition to such a move within Fatah, and some senior leaders believe it may be to their advantage to allow Hamas to take full power, in the expectation that reality will quickly prove the Islamists incapable of governing. Some elements of Fatah may even be inclined to respond violently the outcome, and clashes Thursday outside the Palestinian parliament in Ramallah suggest that there may be more trouble ahead. But Fatah would be foolish to underestimate Hamas' ability to govern: Most of the candidates on their electoral list have post-graduate degrees, and many are experts in various fields of governance. They will certainly be looking to impress the Palestinians, and the wider region, by putting in place a government of competent technocrats.
The election victory has added new incentive for Hamas to maintain its current cease-fire with Israel. It has no interest in provoking the Israelis, because it is now determined to carry out its promises to the Palestinian electorate—promises that are very much based on local concerns over corruption and lawlessness. Before the election, many commentators had asked whether Hamas' entering parliament with a minority share in power would create pressure for the movement to disarm. Now, the situation is turned on its head: Hamas will appoint its own people to run the Palestinian security services, and will make sure that many of its own militants are now drawn in to those forces. And they will have an interest in clamping down hard on violations of law and order by armed groups. It will likely instruct its own supporters to stop bearing arms in public, and it will expect the same from Fatah.
Israel will not be a priority for Hamas for some time. They will allow President Mahmoud Abbas to maintain contact with Israel, but will not enable him to conduct any substantial negotiations—and many Palestinian observers expect that President Abbas may not stay on the job for more than another few months. In the long run, he can't function as president if his government is pursuing a policy at odds with his own.
Hamas already "negotiates" with Israel in a practical sense, although not directly: The current cease-fire is a product of a complicated four-way negotiation between Israel, the Palestinian Authority, Egypt and Hamas. It has an incentive to maintain the cease-fire now, because it needs to implement its domestic program. In the end, a Hamas government will rise and fall not by how it transforms relations with Israel, but how it implements its promises to clean up Palestinian government.