First step, ask your chef instructors!
Second step, ask your placement advisers at the school.
Third step, make a list of ALL the restaurants, commercial kitchens, institutional kitchens within a reasonable driving distance.
Meanwhile, compose a cover letter template that you can customize for a particular inquiry that has:
- What you want to do, i.e. three month externship to complete educational requirements
- Why you want to extern at that particular establishment
- Why they should hire you over any other applicant
- When you will be available and what hours (so as not to conflict with your job)