I don't have time to write the code because it would be too big, but I can give you the base...
Of course, you must have access to a database. You create a database and a table for the movies... It could have 4 fields : id, title, year, number of votes.
When you want to display all the movies, you query MySQL with something like "SELECT * FROM movie_table SORT BY num_votes DESC" (it will select everything, and will sort result according to the number of votes, more votes at top, less votes at bottom...)
When you print result, you put a checkbox with the id of the movie... when submitted, you check which ID have been submitted, then add 1 to the number of votes, ...
To add movies, it's again MySQL queries...
I know this doesn't really help, but that's all I can do...