The following list of phonemes is based on: Klaus J. Kohler, Einführung in die Phonetik des Deutschen, 2nd revised edition, Berlin: Erich Schmidt, 1995; chapters 6.1.1 and 6.1.2.
The example words are links to https://de.wiktionary.org/; the pages there have audio examples. When multiple example words are given, the potential reasons are: to indicate the various spellings of the phoneme in question, or to indicate its different realisations (i.e. allophones, especially for /x/ and /r/).
Note that Kohler analyses /pf/, /ts/ as a combination of two phonemes. The combination /ts/ is interesting in that is is orthographically represented by z, as in Zeit.
I have tried to keep this answer short and to the point. For details, I recommend the Wikipedia article Standard German phonology. If anything is unclear, I advise looking at the transcriptions and listening to the examples at Wiktionary.
Tense (long) vowels
Note that h can be used to indicate that the preceding vowel is long. Less frequently, the vowel is doubled, as in Schnee. Finally, ie always represents long /i/.
- /i/ viel, ihn, Biber
- /y/ Schüler, fühlen
- /e/ Schnee, Zeh, jeder
- /ø/ mögen, Höhle
- /ɛː/ später, zählen
- /aː/ haben, Zahl, Staat
- /u/ Blume, Stuhl
- /o/ Ton, Sohn
Lax (short) vowels
A double consonant (mm, ll, etc.; but also ck and tz) indicates that the preceding vowel is short.
Diphthongs
Reduced vowel
Spelled e; only occurs in unstressed syllables.
Consonants
Plosives
Note that because of final obstruent devoicing, /b/, /d/, /g/ can be realised as [p], [t], [k].
Fricatives
Note that because of final obstruent devoicing, /v/, /z/ can be realised as [f], [s].
The phoneme /x/ is realised as [x] or [χ] following /a/ or a back vowel and as [ç] otherwise.
- /f/ viel, Affe
- /v/ Woche, Virus, primitiv
- /s/ essen, Kuss, Fuß, bis
- /z/ Sonne, Nase, Gas
- /ʃ/ Schnee, später
- /ʒ/ Genie
- /x/ ich, Krach, Besuch
Nasals
Others
The phoneme /r/ is most commonly realised as [ʁ] or [ʁ̞]. Regionally or stilistically, other realisations are possible. For speakers that use [ʁ] or [ʁ̞], /r/ is usually vocalised as [ɐ] in post-vocalic position, i.e. /for/ is pronounced [foːɐ̯] and /bir/ is pronounced [biːɐ̯].