For those who wonder what astronauts said during mission back in ‘70s. NASA has put up a full set of mission transcript from Mercury to Apollo mission. There are many part to choose from such as Onboard Command module, Lunar module (Apollo mission) and ground control, each contain seveal hundreds pages of pdf file.
You can read through the moment Neal Armstrong say “One small step….” or when Jim Lovell say “Houston. We have a problem”
I recommend to get the Apollo 13 mission and compare the one we see in the movies. Some say that the movie’s dialogue is quite accurate.
The link to the transcripts is here