How did the soviet union react to unrest in eastern european countries early on in the cold war?

They responded with force and put down any unrest or uprisings.

Here are two examples:

June, 1953, East Germany.  Construction workers in East Berlin began the protests, demanding an increase in work hours and calling for a general strike.  The call to strike was broadcast over Radio in the American Sector (RIAS) in West Berlin and heard throughout East Germany.  Over a million workers in 700 cities and towns heeded the call to strike on June 17, 1953.  The Soviet Union responded swiftly and harshly, declaring a state of emergency and sending in tanks to larger cities where protests were occurring.
October/November, 1956 - Hungary.Protesters took to the streets in Hungary in October, 1956, demanding freedom from Soviet domination and more democratic political processes. Soviet domination and oppression continued relentlessly, as the USSR sent tanks and troops and crushed the Hungarian Uprising.  Thousands of Hungarians were killed or wounded and over 200,000 fled the country.