Public Performance Rights (PPR) are needed to screen a film to the public. In order to obtain PPR, you will need to contact a licensing service (listed below). PPR fees can vary depending on some factors (numbers of screenings, size of audience, etc.) but generally cost between $200-$400 per screening.
If you want to screen a film for class, please go to the page on In-Class Screenings.
Films that are in the Public Domain are free to screen to the public. There are no comprehensive lists of public domain films, but you can usually determine the public domain status of a film via a quick Google search. Here are a couple reliable sources to help guide selection:
Note: A movie being hosted on Archive.org or YouTube does not guarantee that film is under Public Domain.