After WW2 whole Europe turned left, eg. there was strong communist party even in France.

Support for Communist party in Czechoslovakia was great, SSSR was seen as liberator from Nazi occupation, communists were very active in resistance and Czechoslovak armed forces in exile fought alongside the Red Army. (Also, Czechoslovakia unlike Poland did not have direct experiences with Russian oppression).

Communist were preparing to take over the power already during the war. Immediately after they started to fill important posts in army and police by communists and continued with their propaganda. Most of people believed their promises about justice and prosperity and supported their reforms.

In the first election in 1946 communists won with 40% of votes.

Some might even argue that final coup in 1948 de facto didn't break laws and was legal, despite manipulation with media and threats posed by communist army, armed Worker's Militias and possible Soviet intervention.

What's remarkable is the extent to which the degree of local support in many postwar European countries didn't matter in whether that country eventually 'went Communist.' It was mostly up to agreements made among the Allied Powers (famously, at Yalta). So you have places like Poland, where the Soviet-backed Communist party had to go on a brutal campaign of suppression against non-Communist political parties and the Armia Krajowa in order to secure a postwar Communist system that comparatively few Poles wanted, but which ultimately succeeded because Poland had been included in the Soviet sphere of influence by mutual Allied agreement. On the other hand, Greece and Italy both had very strong local Communist parties, but had been 'reserved' by the US and Britain as being future members of the non-Communist bloc, and were the subjects of intense efforts (in Greece, British backing for the anti-Communist side in the post-WWII Greek Civil War; in Italy, American political and financial support for anti-Communist elements) to make sure they stayed that way.