I have a few thoughts on this. First, I don't think it's extra hard to get an entry level job at a publishing company (about the same as other entry level jobs!). You can look for internships at publishing companies over the summer - research local publishing companies and check each of them for internship opportunities. If you don't have luck there, any other internship in an office setting would also be valuable. You'll want to show that you have solid editing, writing, and organizational skills, and you can do related work in a lot of different office internships. If you have time, you can also consider related extracurriculars like a school newspaper or magazine (not quite as valuable as office experience, but putting them on your resume shows some experience and certainly interest). You might also want to ask your network (family, friends, friends' families, etc.) if they know anyone in publishing, and see if you can have a short phone call or coffee to learn more about the field.
Finally, it's important to consider the fact that the publishing industry is not a growing one. I have had several friends work at publishing companies and then career change, in large part because the industry is not going in a positive direction. (It also typically pays pretty badly compared to other for-profit careers, FYI.) So I'd recommend you also think about other careers that you might like, in order to keep your options open. You could certainly be an editor and do communications work in other settings, such as nonprofits, for example. You can search for "editor" jobs on job search websites, or jobs that require the skill "editing," and read the job descriptions to see what sounds fun, then read the required skills so you know what you need to learn. Just focus on doing activities and finding internships in areas you're interested in and enjoy, and then you'll have skills that relate to work you want to do.