In order to understand Jewish life in Germany, it is important to begin with how religion (in general) is dealt with in Germany.
A basic separation of state and religion does not exist in Germany. In fact, the German constitution obligates the state to be involved in religious matters. Religious communities that are officially acknowledged as such - first and foremost the Catholic and the Lutheran churches - are subject to “public law", which means, in plain English, that they act as state agencies. Their activities are not based on donations (although they are obviously happy to get that too), but on taxation.
The lack of separation between state and religion means, for example, that religion is taught in public schools (“religious instruction shall form part of the regular curriculum in state schools”, says the German constitution). Religion is even an integral part of public television and radio channels. In fact, the most important channels in Germany are state-run channels, funded by a special television and radio tax that each household is forced to pay. Religious communities send representatives to the boards of these public channels, in order to participate in the decisions made about upcoming productions.
Judaism - orthodox, conservative, and reform - is one of the officially acknowledged religions (Islam, interestingly, does not enjoy the same status). It means that unlike Jewish communities in the United States, Germany's Jewish communities are not private associations, but public (state-like) organizations. Their religious, social, cultural and educational activities are based on public funding.
Berlin's Jewish community, for example, receives public funding of about 7 million Euro each year. It employs different rabbis - orthodox, conservative, and reform - all of whom are paid by the same organization. In other words, they all work for the same community. Community members don't belong to a particular synagogue - all the rabbis and all the synagogues of this one publicly funded community are at the service of all community members.
On top of that, the Jewish community also receives tax payments that are taken by the state from the community members. This tax also applies to other officially acknowledged religions and amounts to 9% of one's tax liability (on income, capital gains etc.). So if your annual taxes on all sources of income amount - for the sake of simplicity - to 100,000 Euro, your religion tax would result in an additional amount of 9,000 Euro.
The churches and Jewish communities don't need to bother with collecting this tax. Instead, the state takes the religion tax (just like it does with income tax or capital gains tax) and transfers it to one's religious community. Let's suppose that you open a savings account at a local bank or an investment portfolio with a local broker - your capital gains are taxed at 26,375% and, on top of that, 9% religion tax. For this reason, your bank or broker is legally obligated to ask you about your religious affiliation - and you are legally obligated to disclose it. While other countries consider one's religious affiliation as a totally private matter (and the bank/broker would probably not even be allowed to ask about it), withholding this information in Germany would result in tax evasion on your part. We kid you not.
The religion tax generates additional income for the Jewish community in Berlin, but it is not as substantial as the direct public funding: Most community members are immigrants from the former Soviet Union and thus, to a great extent, anything but affluent. As a result, the community's annual earnings from religion tax are less than a million Euro (i.e. less than 100 Euro per member/year in average).
Last but not least, the Jewish community also has other sources of income, such as donations/inheritance or by renting out property.
Having described the rule, there are also exceptions: Chabad-Lubavitch and the Ronald S. Lauder foundation operate in Berlin outside (or alongside) the framework of the central community, with their own legal entities. These are indeed private associations and thus based on donations, although some of their activities - such as kindergartens and schools - are funded by the general public.
On the federal level, the lack of separation between state and religion means that all public Jewish communities in Germany belong to an umbrella organization called the “Central Council of Jews in Germany" (i.e. not “German Jews" and definitely not “Jewish Germans"). The Central Council of Jews in Germany could be described as the local equivalent of the Jewish Federations of North America, yet with two major differences: It is not voluntary, and it is not private. The Central Council is also based on taxation and its activities are directly funded by the Federal Government of Germany with a yearly budget of 13 million Euro.
Finally, Germany's Jewish communities also run a federal welfare agency with about 8 million Euro in public funding annually.