First, that it will be called "governo Dilma" in Brazil. With a few exceptions, Brazilians prefer to call their elected presidents by the first name. Now let's speculate about the economy, foreign relations, individual rights, and government programs under Dilma.
1 - Brazil's economy is overheated. It seems that the government preference is to cool it by raising taxes. That seems more feasible than lowering expenses, and less insane than either increasing interest rates or letting inflation rise. It is unclear whether anyone in the inner circles of power really understands what they are doing, but they seem to have reached a reasonable conclusion nevertheless.
2 - Dilma does not seem interested in foreign affairs. Expect less activism than under Lula. The silly idea of becoming a permanent member of the UN security council has been forgotten, and Itamaraty will be treated more strictly as a lunatic asylum, in the mold of Sealopra. Proposals to support nuclear weapon development by Chávez and Ahmadinejad are strictly for internal party consumption, as are Samuel Pinheiro Guimarães's consideration that the Axis was the victim of Anglo-Saxon imperialism.
3 - Dilma's platform contained an unstable combination of very progressive proposals for individual liberties, and calls for unconstitutional restrictions to the freedom of press and property rights. Under conservative fire her campaign backtracked, and turned to accusing Serra of being an abortionist supporter of homosexuality. Which in fact is not untrue: he has offered clear defenses of civil unions and abortion rights, although not of changes in the constitution. Do not expect any major advances on individual rights under Dilma. On the other hand, we have no reason to doubt her strong defense of freedom of press.
This will create a problem with the army of psychopaths, racketeers, and failed media entrepreneurs that have been supported by government funds to fire up the PT base. Will Paulo Henrique Amorim, Luís Nassif, Emir Sader, Carta Capital, and others in the self-entitled "alternative media" continue their campaign for "social control" of the press? For sure. Will they succeed in establishing a censorship regime, or will they have to accept government funds instead? The smart money is in the latter. A significant amount, if you ask me. That's another reason why taxes will go up, as seen above.
4 - Under Lula the ministries of education and health, as well as the central bank, were run professionally, specially after the "mensalão" scandals. Besides welfare programs, those 3 were the (qualified) success stories of the last 8 years. The remaining cabinet positions, used as exchange for congressional support, or directly to extract funding for political campaigns, are not very relevant except as money sinks. Administration may even improve under Dilma, who was respected by the professionals in the government.
But she will have to enforce more discipline among the ranks than seen in the last year or so. If corruption scandals force her actions, the Worker's Party depleted ranks of qualified individuals may prove insufficient. The fact that they were conspicuously absent from the presidential and legislative campaigns is a worrying sign.
One more prediction: the next election will not be decided by the result of the World Cup or by the triangulations of politicians and their analysts. It will depend on the phase of the economic cycle in 2014, a variable which science is not able to extrapolate.