How to anonymously and privately purchase Bitcoin through Tor?
First of all, anonimity and privacy are two different things. Bitcoin is designed to be pseudonimous - which is close to anonimity, but instead of being completely anonimous, you're linked to your bitcoin address, or pseudonym.
You cannot make a private transaction on the Bitcoin network, but you can try to be as anonymous as possible.

It is possible to run Bitcoin Core as a Tor hidden service, and connect to such services.
The first step is running Bitcoin Core behind a Tor proxy. This will already anonymize all outgoing connections, but more is possible.

More instructions at github:
https://github.com/bitcoin/bitcoin/blob/master/doc/tor.md