Internships with publishing houses and literary agencies are competitive and sometimes hard to find, but they are worth the effort for writers who want to learn more about the industry. If you're interested in working as an agent or editor (many write as well as edit/agent), and want to learn more about how the publishing industry works, you might consider looking for an internship.
My internships with Entangled Publishing and The Carol Mann Agency are teaching me things I didn't even know I needed to learn, especially things about market, contracts, and the level of writing required to land a publishing deal. It's also fascinating and a great deal of fun to see the creativity and talent of my fellow writers. Of course, it's also amazing to be part of a team responsible for offering on a MS!
Even though internships can be hard to find, there are a number of ways you can increase your chances of finding one. First, follow agents and editors on Twitter. I see internships being tweeted about relatively frequently. You can also subscribe to the list of agents on Twitter here to watch for opportunities like that (and lots of other wonderful information). I heard about both of the internships I eventually was offered through Twitter, so I highly recommend it.
I also recommend checking agency websites and blogs. You can find a list of agent blogs here, and many agencies have a tab with information about internship programs. Others blog about internships when they come available. It's hard to go wrong reading agent blogs, so definitely keep an eye on them.
Finally, use http://bookjobs.com/ Book Jobs has a tab just for internships, as well as one for publishing programs where you can take classes in publishing and receive a degree, credit, or a certificate.
However you do it, learning more about an industry you want to be part of is a great way to sharpen your skills, advance your career, and hopefully even give back to other writers.