How to handle swear words in quote / transcription?

If you're quoting someone, quote them as they said it. We're all adults. In the literature world, we quote swear words and other potentially offensive things all the time and no one bats an eye. I've no doubt other fields are the same.

Personally, if I saw an asterisk or similar, I would presume you interviewed them via chat or email, and they actually self-censored. If it were a printed text, I'd think it a part of the edition you used.

In research, you should quote them verbatim. Editing, or censoring, swearing is wrongly representing your research subjects and is thus a form of scientific misconduct. If you need to edit the quote for specific audience you must make it clear that you have done so:

It's just so [obscenity] slow, it really [obscenities] me off.

With a note saying that you have edited the text to remove swear words. Partial censorship such as you used above (e.g. f*ck, c*nt) is both utterly pointless and misleading; either completely remove the word (indicating where you have done so) or quote properly:

It's just so fucking annoying; it really fucks me off.

I'm a history student currently working with oral history. You should not smooth anything on a transcript — when quoting you should do exactly as said or written. There are certain ways to indicate that something is a grammar mistake or a phonetic(?) transcription to clarity that there's no mistake on your part; usually those things are put in foot notes.

I'll edit this later to give you some resources for that, but for now if you put any notes make sure to do it as a footnote. You can use the brackets too, they indicate some comment of the author outside the context of the quote.