1) Shutting down big torrent sites by modifying laws (for example, making linking to torrents illegal)
2) ISPs blocking the big sites domains like piratebay
3) Fining consumer users (who failed to be anonymous with VPNs and other tools)
4) Attacking the big users of the network (seed boxes, pirate groups or in the context of BTC: miners)
The other approach is make the conversion of state currency into BTC illegal. But the implications of that are unclear. Would people adopt a different crypto-currency? Would all crypto-currencies be banned? Could a BTC black market still exist like drugs?
I think more than likely it would be like torrents are now: a large amount of the tech-savvy population uses them and loves them, but a lot of people are afraid they'll get sued or have a letter written to their house from their ISP (which means nothing), and would rather just pay $7.99/month for a worse selection on Netflix and maintain a peace of mind.