Than there is your registration on localbitcoin. You would need a truely anonymous email address.
And the site behaves really poorly if you try to use it over tor.
If you do the cash transfer in person, the seller might be able to identify you.
If you don't do it in person you would have to send it via some money transfer service.
It is allways hard not to leave traces when you interact with something / someone.
Edit: As 'austerity' stated: 4. Do not accidentally leak your identity in one of million possible ways. [...] But #4 is next to impossible.
