I would like to use this font for a movie poster but, I don't know whether I am allowed legally. Am I allowed to use it or do I need permission?

Which font? Anyway, always ask the author.

SF Movie Poster Condensed, how would I ask the author?

You can contact the author via his website: http://www.shyfoundry.com/index.html

Look at the Readme.txt file in the Zip file you downloaded.