It was damn hard. The borders were guarded and carefully monitored. The police had mirrors they could use to look underneath trains to see if people were hiding under the trains as a means of escape, besides the trains being very carefully searched. Papers were thoroughly checked. 125 people were killed trying to get past the Berlin Wall--it was so hard that people risked their lives on a regular basis to do it, knowing full well that getting killed was a strong possibility. Before the Berlin Wall was built, though, it was easy--you could travel more or less freely from one area to another between East and West Germany. And while you couldn't travel outside of the Soviet Union without difficulty, you could travel from the Soviet Union to East Germany with a little more ease, though you still needed all kinds of permissions.

That said, I've met people who've done it. One thing they could do, for example, is get a visa to go from the Soviet Union to a country that shared a less closely guarded border. Some could get a visa to go to another country for the day, for example, and then they'd just stay and seek asylum. Some were able to get a visa for a legitimate purpose--an academic conference, an educational opportunity, or an athletic event. Once in the West, they could defect... but they'd not be able to see their family or friends ever again, as far as they knew. And there might be repercussions on their family and friends for their defection. So it was a tough decision. A number of athletes (tennis stars, Olympic athletes, chess players), artistic performers (musicians, dancers, artists), and scholars were able to defect, though at great personal cost. I knew a Czech citizen who was on holiday in Austria when the "Prague Spring" closed the borders. She couldn't go home then, and then she just ended up staying and making her way to the US. Back then, it was easier to get a visa for a short while. The borders tightened up later, and athletes, musicians, dancers, etc. eventually had greater security controlling their every move so they'd have no opportunity to defect, following the many embarrassing defections that had occurred earlier. Olympic athletes were carefully guarded. Another example is two South Koreans--a director and an actress--who were kidnapped to North Korea by Kim Jong Il and forced to perform for him, for years. Eventually, he began to trust them and they were taken to Cannes for their movie premiere. They were able to get enough distance between themselves and their handlers that they could flee. Here's a list of some of the methods people used. https://en.wikipedia.org/wiki/List_of_Soviet_and_Eastern_Bloc_defectors (usually I wouldn't mention a Wikipedia page but this is the kind of question that I think lends itself more being answered by a list).