How should I translate an ablative absolute? I've never managed to get it.

You should always start by translating it with 'with,' so for example, 'with the man having laughed,' 'with the man laughing,' or 'with the man being about to laugh.' If you're not sure of the tense, see what makes most sense with the context. Then, you should try to see if you can replace the 'with' with something else. So, for example, 'because the man had laughed' or 'while the man laughed.' If you're not sure how to replace the 'with' just leave it as 'with.'