Going on vacation inside the Soviet Union was essentially the same as in any other country. As long as you could afford train/plane tickets and accommodation, there was no problem. But going on vacation outside the country was generally not possible, unless you had a business reason to travel. If you had to travel abroad, usually you wouldn't be by yourself, it would be with a group and there would be a chaperon to supervise things.

Depends a lot on time period, and country. Travel within a country, like the USSR, was pretty easy to do, but if you were doing it for vacation(like to visit a Spa) that would be arranged by your trade union or work unit.

Travel within eastern Europe was doable. It was pretty common for East Germans or Poles to take holidays in Bulgaria, for example, and vice versa. In the 1960s people from Czechoslovakia would occasionaly bus to Vienna for hockey games.

Yugoslavia was one of the best countries for freedom of movement, and they could travel pretty much anywhere. Yugoslavia made a lot of money from guest workers abroad.

On the other hand, if you lived in Romania or Albania: forget it.