Nothing. Shut the fuck up. Ive seen a lot of posts about cleaning house and getting a lawyer which is good advice, but I think there should be more about how to talk to the police, which means, don't.
Since Im just some guy on an alt account, take it from this guy who is a lawyer: https://www.youtube.com/watch?v=i8z7NC5sgik
Another lawyer who sometimes posts to reddit, /u/kenpopehat: https://www.popehat.com/tag/shut-up/
He's a former federal prosecutor, and harvard educated. He makes bank charging huge fees to white collar suspects. He knows what hes talking about. His best and free advice is to shut up.
(Disclaimer: Im new to the whole DNM scene trying to find a specific vendor, who I still havent found. But I am not new to civil liberties. Know your rights and use them. Also, this advice applies to Americans. Other countries may be different.)
Edit: Some people have pointed out you should explicitly invoke your right to remain silent. This is most correct. In fact, you should also explicitly invoke your right to an attorney while you're at it. A simple phrase "I invoke my right to remain silent and I invoke my right to have an attorney present for any questioning" should work. But even that can be a mouthful if a bunch of goons just broke down your door and shot your dog. If you can't manage that, just saying 'lawyer' might work. But whatever you do, dont interact with them. Dont explain anything. Sitting there quietly is still better for you then opening your mouth.
Absolutely. And to expound on this just a little, don't even deny anything. If you haven't been arrested yet (even if they 'detain' you), the only two things which should come out of your mouth are: "Am I free to go?" and some version of "Me. Lawyer. Now." If you have been arrested, the latter.