To be properly anonymous you'll need to pay with cash. That means paying someone in person, and probably winding up in a bag somewhere, or depositing it in someone's bank account and the bank will make sure you end up in a bag instead considering the amounts at play.
By paying in cash or going to the bank depositing the fund has actually revealed such person identity and that violated his/her motive to go anonymous. I think the best way to do that is to register on the most good exchanges like
Bittrex, Binance, Polonix etc. Though he might not be able to buy less than below 1BTC if he doesn't do KYC and even if KYC is done, he might not be able to buy more than 2-5BTC a day. That means he has to wait a little long before he could buy the really amount he wanted to buy.
That will not work, at least Poloniex and their new policy don't allow anon users anymore.
I not sure if local bitcoins allow it, but if i would like to do that i think the right way would be:
1.-Download TOR.
2.-Open an account on Localbitcoins.
3.-Make a deal for Cash.
4.-Meet with the seller, bring the cash and give him your btc addy.
By the way, if you really want to be anon, i recommend you to not use bitcoin, you should better use Monero or Zcash.