@Mech123 You will follow your recommended academic plan (https://rap.psu.edu/mechanical-engineering-university-park) and get a C or better in these courses (https://advising.psu.edu/entrance-major-requirements-college-engineering-2017) as well as a GPA requirement (currently 3.20 but check again when they upload the page for people entering Fall 2017). You will then apply for your major, probably during your third or fourth semester.
Note: it’s not much of an application process. If you have the courses and the GPA, you’re guaranteed a spot.
(Thanks for the tag, NASA)