In Hungary leftist parties were popular, the communist party got about 17% in 1945 (2nd place, but the winner got 60%), and won the election with 23% in 1947. The elections were rigged in 1947, it´s hard to say how much would they have gotten in a clean election. In 1949 the ballots had only two option printed on them: Popular Front of Hungarian Independence and against. (actually you had to make an X only if you were against the only runner, in the other case you just had to put the ballot into the box as you received). Edit: Which meant, that in an already suspicous and fearful society hardly anyone dared to go into the booth, because it meant you vote against the communists. So people just went straight to the box to cast their vote "freely".

The political struggles didn´t really reflected popular opinion, it was mainly about the Hungarian Communist Party using the Ministry of Interior (and through it the secret police) to discredit, bully and chase away the leadership of other parties, and destroy or assimilate those parties at the end.

As of communism, the leftist reforms introduced early on were popular eg.: land redistribution. But later on, especially after 1949 with the introduction of what was presented as the first steps toward communism (collectivization, nationalization of not just the large industrial enterprises, but even small family shops, outlawing every other party, total control of the media, interference even with family matters) the regime became less and less popular, which brought on harsh repression first, reform steps later, and finally the 1956 revolution.

So, after WWII leftist ideas were popular (there were only leftist and liberal parties), as there was a lot of reforms long due (decades). The communist party was one of the largest ones, but when communism was introduced the population turned against the leaders rather quickly.

But bear in mind, communism was perceived by the majority of the population, not studied. Not the best example, but I can´t think of a better one right now: something like democracy in post-soviet russia, many were in accordance with the ideas and goals, but virtually all loathed the reality.

Edit: And to answer the second part of your question. Yes, communism was imposed by the Soviets. They had their local communist party, with their local leaders and local secret services, but those people never could have grabbed the power without the soviet military presence and the deep involvement of the soviet advisors in the ministry of interior.