Most campus organizations will not allow students to apply during the summer, so you may have to wait until you arrive on campus to apply for a job. Many of them will have informational booths during the first few days of school as well to explain their open positions and how to apply. Some organizations will let you apply at their booth.
Here are some places that you could look for a campus job.
The student employment website has all the basic information on student employment at Notre Dame. It includes a link to the Notre Dame Job Board, a list of frequently asked questions, and resource links to forms.
The Job Board is the most extensive list of available positions on campus, though not all possible jobs are included; many of the ones that aren’t are in specific departments and are listed on the department’s website. Those generally require that applicants are in that college in order to fill the position.
These positions include those at the Huddle House, all restaurants in LaFortune, the North and South Dining Halls, Reckers, and as banquet servers.
This website includes positions as event assistants for the LaFortune Student Center, positions reserved for upperclassmen, and more links to food service jobs.
This site allows you to apply to available positions online. It requires more thorough searching to find a job specifically for students, as the website lists all jobs open at Notre Dame, but it includes filters for easier management.
The Development Phone Center hires students to call alumni and Parents and Friends of the University to raise money for the Annual Fund. Follow the link to see a full job description and to fill out the application.
The Office of Information and Technology is looking for student consultants to help assist their fellow classmates, faculty, and staff with their computing and technology issues. Follow the link to see a full job description and to fill out the application.
This page has descriptions of all positions available through RecSports. Here is the application form.