If you're looking for a specific film, do a title search using the title of the movie.
If a title search fails, use a keyword search in the library search and type in the title of your play. Your play may be in a collection of plays; a keyword search will search the table of contents of some of those collections. Again, note the call number and locate it in the library stacks.
Browse the stacks in the library search call number area: PN 1997 (Main Library 4A)
Are you looking for plays by a certain playwright?
If you have a specific playwright in mind, or scriptwriter (for screenplays), do an author search in the library search.
Another free site for film scripts posted on the Internet. Note that there are likely to be copyright violations involved with unauthorized scripts being presented.
Can't find what you want?
Theatre Arts instructors also have copies of monologue collections for your use, so consult with them if the library's copies are checked out. You can also find a number of used monologue books at places like Bookmans Entertainment Exchange.