1) Mine the bitcoins ("create" them)
The pool will likely have a lot to say about you. VPNs might help, but then you need to trust them. How do you pay? Is it a honeypot? Tor might be an option, but latency comes into play. If going solo, variance is a bitch, plus you need to worry about your ip address exposed again.
2) Transact cash (untraceable) for bitcoins, via a service like localbitcoins.com which brings buyers and sellers together.
...and government and other agents, too.
3) "Clean" bitcoins. Someone may be able to infer that you initially purchased some amount of bitcoin and sent it to some particular public address, but from there a seed of doubt can be planted. "Plausible deniability".
Yes. This is an important and often ignored detail.
Overall, it takes careful planning and hard work in proportion to the value of your privacy as a target. My effort would be much smaller than that of a politically exposed person or a big-time drug dealer or a terrorist.
