When the arriving numbers of refugees increased, Merkel repeatedly said 'We can do it' to critics and supporters of her asylum policy. She also mentioned this in her New Years Eve Speech. I don't want to discuss the pros and cons of her policies but rather get to know what concrete measures were taken / are likely to be taken in the near future.
Hopefully the analysis I have found is current. Quite possibly, they will be or will have already implemented new measures for dealing with integration.
German integration following a 2005 law uses a "two track approach". First, immigrants are offered integration courses. These courses include "600 hours of instruction in German as a foreign language, and a 30-hour introduction to German civilization and culture. There is a required test at the end of the course (Petra, 3).
Immigrants are required to attend these courses if they received their first resident permit after January 1st, 2005 and any of the following; are an employee, are waiting for subsequent family members to immigrate, are here for humanitarian reasons (refugees I believe) or are long term residents (BAMF). Germany has been routinely increased the funding for these courses (Petra, 3).
Another integration measure is the offering of 'Migration Counseling for Adult Immigrants' and 'Youth Migration Services'. These services are put together at the State level in Germany rather than Federal level as the integration courses are (Petra, 3). Meaning, the content and effectiveness of the courses may vary widely.
As always, integrating immigrants, especially those with quite different backgrounds than the majority population, is difficult. As a sidenote, I am personally more hopeful for successful integration of this round of immigrants than previous rounds. In the past, large immigrant populations were assumed to only be temporary "guest workers". In Germany, particularly immigration that occurred between 1955 and 1973 (Petra, 1). This was a common theme among European countries during that time. They were not anticipating that the immigrant populations would stay in the country.
Because that round of immigration was considered temporary, few measures were taken to integrate that round of immigrants into the country. You can imagine that allowing immigrants to slowly become a significant part of your labor force while not attempting to integrate them would be a bad idea. In this round of immigration, by contrast, serious measures are being taken to attempt integration of these immigrant (refugee) groups. Hopefully, it will work better but you cannot be completely certain.
There are two answers to the question: Paper, and reality.
On paper, Bill has given a good introduction. There are considerable efforts on integration courses, finding working opportunities, moving refugee children into regular schools as soon as they speak the language, etc.
However, in reality the most likely answer is: There will be no integration. Not in the sense that people might expect from countries like the US, where everyone has some ancestors from Europe, Asia or Africa, but aside from a family tree and some distant relatives, the "american" identity has overcome the heritage.
German cities already have regions that are similar to the various Chinatowns around the world, except that they are turkish or arabic, not asian. These came into existence decades ago without intentional planning, simply by enough guest-workers with arabic heritage (Turkey being the main source of guest workers) living in the same region and then non-arabic inhabitants moving out. It is very likely that those refugees who stay will likewise be pulled into those regions. There is little integration in there, some inhabitants speak no german at all, and the sight of children accompanying their parents to the government office to translate for them is quite common. There was a hope that these children would be better integrated, but with the refugees, a fresh wave of people who did not grow up and go to school in Germany (thus picking up the language from early age) arrived.
Germany to this day does not understand itself as an immigration nation the way that the USA, Canada or Australia do. As such the integration programs are recent and not well understood, their effectiveness unproven. In addition, the culture in Germany has switched from an initial welcoming and friendly attitude to somewhere between cautious and outright hostile, mostly due to simply too many refugees and the failure of the German government to address the people's reservations aside from some snide "we will manage" remarks. This creates a second barrier to integration, this time from the other side.
There is, however, also a low-level, unstructured form of integration. Many Germans still welcome the refugees and interact with them, supporting them and in the process forming personal bonds. This might yet turn out to be more successful than government-mandated school-like programs.
The proper answer to "how" is probably a mix of government efforts and personal efforts, but the real question is "how much".