To access and manipulate files in a Perl program, there is a three step process: 1. Open the file using the open() function, which establishes access to the file. 2. Read from or write to the file as needed. 3. Close the file using close() to release access when done. The document provides examples of opening files for reading, writing, and appending using open() and specifies modes like > and >>. It also gives a short script that demonstrates copying the first three lines of one file to another as an example of file handling in Perl.