There is an article in English Wikipedia that describes the different regional pronunciations of latin.
In the German spoken area there are two different pronunciations important (both linked articles are in German language):
In music (i.e. for singing christian masses from Italian composers) there is also important the Italian pronunciation of Latin.
The German school-pronunciation is a mixture of the reconstructed pronunciation and the usual German pronunciation. But in a scientific context the preferred way to pronounce latin words is the German pronunciation.
What are characteristics of German pronunciation?
Note, that in the middle and northern parts of Germany [b], [d] and [g] at the end of a word become [p], [t] and [k] (Auslautverhärtung)
There is also an article in Wikipedia that deals with the pronunciation of old Greek in German.
Here also exists an attempt to reconstruct the old pronunciation, but what you will hear in German spoken countries is a little bit different.
Biggest difference: Sounds, that do not exist in German language (like [θ]) will not be used in German pronunciation.
There also is no difference in pronunciation of θ and τ. Both are spoken as an aspired [tʰ]. (T is always aspired in German)
Generally spoken π, τ and κ are always aspired (i.e. [pʰ], [tʰ] and [kʰ] instead of [p], [t], [k])
Σ and ζ are pronounced like latin s and z (see above).
Χ most often is pronounced as [x] (like ch in German »Dach« = [dax]) but sometimes also like c in latin language (see above)
The greek vowels are pronounced like their Latin counterparts.