The letter ד represents the phoneme /d/. In Modern Israeli Hebrew, this phoneme is pronounced [d] (like the <d> in English dog).
In the Masoretic Text, the letter ד takes a dagesh (דּ) not only when geminated, but also at the start of a word or after a consonant. In Yemenite Hebrew, it is pronounced [d] in those contexts, and [ð] (like the <th> in English this) in other contexts; it is commonly believed that the same was true in Classical Hebrew.
In Modern Israeli Hebrew, the sound /ð/ (like the <th> in English that), which occurs in various foreign phrases and proper nouns, is commonly written ד׳(dh).
The letter ד does not have many "grammatical" uses — it mostly occurs only in the "main" part of a word — but one exception is in hitpa'el verbs (and derived nouns) where the first letter of the root is ז(z); for example, one says הִזְדַּקֵּן(hizdakén, “to grow old”) rather than *הִתְזַקֵּן(hitzaken).
