IPA transcription of kana づ please: I think it will be [dzɯ].
This description is written from Toukyou-area Japanese / 標準語; it applies through most of the rest of Kantou and most of Kansai and Chuugoku as well (with the major exception of the Unpaku dialect around the former Izumo province).
The consonant will be [z] or [dz] depending on speaker and context. ず varies similarly, and there is no way to distinguish between the two.
The vowel has no agreed-upon IPA transcription. It's not [ɯ] because it does involve bringing your lips together, but it's not [u] because it doesn't involve pushing your lips outwards or pulling the corners of your mouth together. Some (I don't remember who) have described it as a 'compressed' vowel rather than a rounded vowel; you bring your lips together but not as much as with [u], and without rounding them at all (the corners remain basically in place).
I have heard it vary, though, anywhere from really quite similar to [u] (especially in more choral singing; I wonder if this is European influence) to something that's as far forwards as [ʉ]. Mostly it seems to be in the middle, though, conforming fairly well to the above description.
Elsewhere in Japan:
Part of southern Shikoku (Kouchi, for example) preserves the original [d] in free variation with [dz], contrasting with the [z] in ず. Kagoshima and eastern Kyuushuu contrast just [dz] with ず's [z].
In Touhoku/Hokkaidou and some parts of the Unpaku area, づ・ず have further merged together with ぢ・じ thanks to /i/ and /u/ merging into [ɨ] (I think, Japanese sources mostly transcribe it unhelpfully as 'ï') after /t d s/ (and maybe /n/?). This has removed the trigger for the /s z/ → [ɕ ʑ] change, and all four kana vary in pronunciation between [zɨ] and [dzɨ]. Other parts of the Unpaku area have shuffled around /i/ and /u/ rather than merging them and mostly leave づ as [du] (probably not with actual [u] but the Japanese version described above).
Narata in Yamanashi prefecture apparently pronounces づ with [ɖ], oddly enough; the whole yotsugana series (じ・ぢ・ず・づ) is the rather remarkable [ði ɖʐi ðu ɖu] (with the same caveat about 'u').
The same as ず, can be /dzu/, /dʒu/ or /ʒu/.
Source: https://ja.wikipedia.org/wiki/づ (Cited by @istrasci)