You can't talk about the pronunciation of »d« without talking about »t« too.

Rule of thumb:

• In German the letter »d« is pronounced as [d] (voiced alveolar stop)
  like in these English words:
  • down [daʊn]
  • dash [dæʃ]
  • sand [sænd]
  • lid [lɪd]
• In German the letter »t« is pronounced as [tʰ] (aspirated voiceless alveolar stop)
  like in these English words:
  • time [tʰaɪm]
  • tick [tʰɪk]
  • fat [fætʰ]

Some brief information about [tʰ]:

1. Do not mix up the aspirated t [tʰ] (like in tee [tʰiː]) with the two english th-sounds [ð] (like in "this" [ðɪs] and [θ] like in thief [θiːf]. The small superscripted h stands for a short breathing sound after the stop-sound. This is called "aspiration".
2. In German and in English the sounds [p], [t] and [k] normally are aspirated ([pʰ], [tʰ] and [kʰ]), but many dictionaries (among them wiktionary) doesn't show this aspiration. [p], [t] and [k] are not aspirated in Italian for example, which gives [p], [t] and [k] a softer sound in Italian words, but still different from their voiced siblings [b], [d] and [g].

But there is more to say:

Final-obstruent devoicing or terminal devoicing (in German: Auslautverhärtung)

This is a mechanism in many, but not all languages. Turkish has this mechanism, English doesn't have it. In German it depends on the region. In most parts of Germany (north of Bavaria) you can hear this terminal devoicing. In Austria you won't hear it.

This mechanism turns [b], [d] and [g] into [p], [t] and [k] if it would be the last consonant of a syllable.

So in Hannover, Hamburg and Berlin (all three in the northern parts of Germany) »d« at the end of a syllable will be pronounced as if it was a »t« (but I think without aspiration, I'm not sure about this point):

• Fahrrad [ˈfaːɐ̯ˌʀaːt]
• Schwimmbad [ˈʃvɪmbaːt]
• Südfrucht [ˈzyːtˌfʀʊχtʰ]

But you don't hear this final-obstruent devoicing in the south. In Bozen (in the north of Italy), Graz and Vienna (both in Austria) you hear:

• Fahrrad [ˈfaːɐ̯ˌʀaːd]
• Schwimmbad [ˈʃvɪmbaːd]
• Südfrucht [ˈzyːdˌfʀʊχtʰ]

There even is another regional difference in the pronunciation of »d« and »t«:

In the south, the [tʰ]-sound is much softer and even less aspirated than in the north. It is very close to [d]. This is true for standard pronunciation, but the effect is even stronger in dialects.

Take the word »Teppich« (carpet) as an example. If you look for the pronunciation in a dictionary, you will find the northern standard, which is:

[ˈtɛpɪç] or [ˈtʰɛpɪç]

This means: a hard and voiceless t, a short e, and a hard and voiceless p

If you listen to people in Vienna, speaking their local dialect, you will hear:

[ˈdɛːbɪç]

a soft voiced d, a long e, and a soft voiced b

And this local dialects have a strong influence to pronunciation in standard German. So in Austria you will find, that also t often is pronounced like d. In Austria there is not much difference between Dorf (village) and Torf (peat, turf) or between Mandel (almond) and Mantel (coat).

The fact, that t and d in Austria almost (not exactly!) sound equal, makes it harder for Austrian kids to learn the correct spelling of words, and therefore they learn the names »weiches D« (soft D) and »hartes T« (hard T) for the letters. If in Austria an officer asks you to spell your name, and your name contains d or t, then the officer might ask you

Mit weichem oder hartem D?

Whereas it is unclear if the letter at the end of the Question should be written as »D« or »T«, because specially in this question, they really sound exactly equal.

_{This part is off-topic, i.e. not part of the "official" answer, but is is an interesting episode showing how similar T and D are in Austria:}

_{Adolf Hitler was born in Braunau, in Upper Austria (one of the nine states of Austria), near to the border to Germany, because at the time when he was born, his father, Alois Hitler, was a customs officer, working at the Austrian-German checkpoint. Alois Hitler and his wife Klara both was born near Gmünd and Zwettl in the northern parts of Lower Austria (another Austrian state). Alois was born as Alois Schicklgruber, because his mother (Anna Maria Schicklgruber, Adolf Hitlers Grandmother) was not married when she gave birth to Alois. She later married a man, who was thought to be the father of Alois (which still is matter of debates, because also a jewish salesmen from Graz named »Frankenberger« could have been the father of Alois and therefore Grandfather of Adolf Hitler).}

_{But the name of this man was not Hitler [ˈhɪtlɐ]. His name was Johann Georg Hiedler [ˈhɪːdlɐ]. Pronounced with a long i, and a soft and voiced [d].}

_{Johann Hiedler never adopted his wives son Alois Schicklgruber. But when Johann died, there was no legal heir. To make Alois Schicklgruber the legal son of Johann Hiedler, he had to change his name. But because in Austria Hiedler and Hitler almost sound equal, the registrar did not write Hiedler into the documents, but Hitler.}

_{And so Alois Schicklgruber was renamed to Alois Hitler, and so the name of his son is neither Adolf Schicklgruber, nor Adolf Hiedler, but Adolf Hitler.}