How would that interning process work? My kids are still very, very young, but I'd love to know how to get them started off on the right foot in a career like that if they were so inclined.
So we have a pretty formal intern program here. We actually put out a job description and accept resumes from college students in the area in whatever discipline we have an open internship position for (engineering, marketing, sales, product management, etc.) so we'll get students with engineering, marketing or business backgrounds. Try doing a job search in your area under "intern" and see if companies have similar programs in your neck of the woods. Bigger companies have more formal programs, while smaller companies might just hire on someone with less of the fuss we put them through here.
The resumes are usually 1-page or so detailing out achievements in HS and such. Honors programs, GPA, extracurriculars, clubs, sports, job experience (if something worthwhile), volunteer work, etc. We'll actually bring them in and do a quick interview. Nothing hard, just a 15-30min meet and greet as we don't expect them to really know much, but at the same time you want to meet the person who will be part of your team. These aren't top kids from top schools either. Most are pretty average kids who live locally who are actually putting themselves out there to try to get ahead.
From there, they come in, get a formal orientation, meet up with their manager (I have two interns under me this summer), and we put them to work for the summer. Typically running out and getting coffee is NOT what they do for us. I'll give my engineering interns actual CAD projects and expect drawings out of them. While they are doing work for us, we try to teach them and get them engaged as well by giving them a diverse, and interesting workload.
It's also a paid internship here, with starting pay this year at $18.
As far as I know, every senior last year got a job when they graduated. My company hired on at least one of them from last years pool. One intern I had actually worked for 3 different companies through college and had a VERY good resume when he graduated. He got scooped up right away.
FYI: I did not go through such a program myself. I still managed to do ok, but getting my foot in the door for that first interview was a bit harder than if I went through an intern program like ours.