In "democratic" countries government can do the following:

Regulate bitcoin.

Require exchanges in the country to follow the Know Your Customer rules.

Legislate unfavorable taxations laws - taxing it like commodity instead of currency.

Require to follow expensive procedure to open exchange - like New York license.

Create massive propaganda in mainstream media by claiming that it is used for money laundering, black market and by ISIS.

In non democratic countries:

Make it illegal to open a bitcoin exchange. 

Try to actively track bitcoin transactions and locate the state citizens involved in bitcoin transactions and prosecute them.

Off course all of these can backfire. In democratic countries - by switching bitcoin activity to more tolerant countries and thus letting them to enjoy the huge competitive advantage from allowing bitcoin related technology to develop freely.

In non democratic countries - by adding incentives for bitcoin to evolve and become even more oppression resistant. Also in those countries - whatever the government fights - immediately becomes something that everybody assume is good to have.

Those techniques cannot stop bitcoin and will fail miserably. Even if this was a global attempt to ban bitcoin - it would only slow down the adoption rate and force bitcoin to evolve even more rapidly.

Bitcoin is information - it cannot be banned. Once people realize it is possible - it cannot be undone.