What steps did the Soviet Government take to repress the protests in 1970s and early 1980s?
The most common thing that the Soviet government did to dissidents at this point in their history was to jail them. They did not do as much executing of prisoners as they had during Stalinist times. Even so, they did not really tolerate dissent.
One example of this is what happened to the dissident Natan Sharansky. Sharansky wanted, among other things, to be allowed to leave the USSR to live in Israel. In 1977, Sharansky was sentenced to a 13 year term in prison for supposedly being an American spy. In addition, the government used similar tactics like putting dissidents in mental hospitals or exiling them within the country. There were also, of course, less formal intimidation tactics like having dissidents beaten.
Overall, the main way of repressing dissent was to threaten dissidents with various forms of loss of freedom.